Need help with different errors

HEllo! Could someone help me sorting out some errors in my opencart 1.5.4.1 store?

Posting error.log:
2013-06-29 8:04:46 - PHP Notice: Undefined index: zone_id in ******/*******/******/catalog/controller/account/register.php on line 423

2013-06-29 22:01:58 - PHP Notice: Undefined index: zone_id in ******/*******/******/catalog/controller/account/register.php on line 423

2013-06-29 23:11:49 - PHP Notice: Undefined index: zone_id in ******/*******/******/catalog/controller/account/register.php on line 423

2013-06-30 11:25:52 - PHP Warning: file_get_contents(******/*******/******/system/cache/cache.product.total.2.0.1.3c44d9d8760b577f7d38f89aeb05c3cb.1372595104) [<a href='function.file-get-contents'>function.file-get-contents</a>]: failed to open stream: No such file or directory in ******/*******/******/system/library/cache.php on line 9

2013-06-30 22:00:23 - PHP Notice: Undefined index: zone_id in ******/*******/******/catalog/controller/account/register.php on line 423

2013-07-01 13:52:58 - PHP Warning: Cannot modify header information - headers already sent by (output started at ******/*******/******/catalog/language/norwegian/checkout/cart.php:1) in ******/*******/******/vqmod/vqcache/vq2-system_engine_controller.php on line 28

2013-07-01 13:52:58 - PHP Warning: Cannot modify header information - headers already sent by (output started at ******/*******/******/catalog/language/norwegian/checkout/cart.php:1) in ******/*******/******/vqmod/vqcache/vq2-system_engine_controller.php on line 29

2013-07-01 13:57:47 - PHP Warning: Cannot modify header information - headers already sent by (output started at ******/*******/******/catalog/language/norwegian/checkout/cart.php:1) in ******/*******/******/vqmod/vqcache/vq2-system_engine_controller.php on line 28

2013-07-01 13:57:47 - PHP Warning: Cannot modify header information - headers already sent by (output started at ******/*******/******/catalog/language/norwegian/checkout/cart.php:1) in ******/*******/******/vqmod/vqcache/vq2-system_engine_controller.php on line 29

2013-07-01 16:58:16 - PHP Notice: Undefined index: HTTP_USER_AGENT in ******/*******/******/catalog/model/tool/online_plus.php on line 9

2013-07-01 17:27:39 - PHP Warning: unlink(******/*******/******/system/cache/cache.product.total.2.0.1.cda58047e25e3c41f1dde3104b2bdd8b.1372699633) [<a href='function.unlink'>function.unlink</a>]: No such file or directory in ******/*******/******/system/library/cache.php on line 18

2013-07-01 17:27:39 - PHP Warning: unlink(******/*******/******/system/cache/cache.product.total.2.0.1.3c44d9d8760b577f7d38f89aeb05c3cb.1372703212) [<a href='function.unlink'>function.unlink</a>]: No such file or directory in ******/*******/******/system/library/cache.php on line 45

2013-07-01 17:27:39 - PHP Warning: file_get_contents(******/*******/******/system/cache/cache.product.total.2.0.1.3ab6383f48f3f14cf1e59231406988c8.1372699633) [<a href='function.file-get-contents'>function.file-get-contents</a>]: failed to open stream: No such file or directory in ******/*******/******/system/library/cache.php on line 9

2013-07-01 19:06:24 - PHP Notice: Undefined index: zone_id in ******/*******/******/catalog/controller/account/register.php on line 423

2013-07-01 19:30:36 - PHP Warning: Cannot modify header information - headers already sent by (output started at ******/*******/******/catalog/language/norwegian/checkout/cart.php:1) in ******/*******/******/vqmod/vqcache/vq2-system_engine_controller.php on line 28

2013-07-01 19:30:36 - PHP Warning: Cannot modify header information - headers already sent by (output started at ******/*******/******/catalog/language/norwegian/checkout/cart.php:1) in ******/*******/******/vqmod/vqcache/vq2-system_engine_controller.php on line 29

2013-07-01 19:30:40 - PHP Warning: Cannot modify header information - headers already sent by (output started at ******/*******/******/catalog/language/norwegian/checkout/cart.php:1) in ******/*******/******/vqmod/vqcache/vq2-system_engine_controller.php on line 28

2013-07-01 19:30:40 - PHP Warning: Cannot modify header information - headers already sent by (output started at ******/*******/******/catalog/language/norwegian/checkout/cart.php:1) in ******/*******/******/vqmod/vqcache/vq2-system_engine_controller.php on line 29

2013-07-01 19:32:56 - PHP Warning: Cannot modify header information - headers already sent by (output started at ******/*******/******/catalog/language/norwegian/checkout/cart.php:1) in ******/*******/******/vqmod/vqcache/vq2-system_engine_controller.php on line 28

2013-07-01 19:32:56 - PHP Warning: Cannot modify header information - headers already sent by (output started at ******/*******/******/catalog/language/norwegian/checkout/cart.php:1) in ******/*******/******/vqmod/vqcache/vq2-system_engine_controller.php on line 29

2013-07-01 21:22:58 - PHP Notice: Undefined index: HTTP_USER_AGENT in ******/*******/******/catalog/model/tool/online_plus.php on line 9

2013-07-01 21:27:14 - PHP Notice: Undefined index: HTTP_USER_AGENT in ******/*******/******/catalog/model/tool/online_plus.php on line 9

2013-07-02 11:07:43 - PHP Notice: Undefined index: zone_id in ******/*******/******/catalog/controller/account/register.php on line 423

2013-07-02 13:53:30 - PHP Warning: Cannot modify header information - headers already sent by (output started at ******/*******/******/catalog/language/norwegian/checkout/cart.php:1) in ******/*******/******/vqmod/vqcache/vq2-system_engine_controller.php on line 28

2013-07-02 13:53:30 - PHP Warning: Cannot modify header information - headers already sent by (output started at ******/*******/******/catalog/language/norwegian/checkout/cart.php:1) in ******/*******/******/vqmod/vqcache/vq2-system_engine_controller.php on line 29

2013-07-03 6:54:58 - PHP Warning: Cannot modify header information - headers already sent by (output started at ******/*******/******/catalog/language/norwegian/checkout/cart.php:1) in ******/*******/******/vqmod/vqcache/vq2-system_engine_controller.php on line 28

2013-07-03 6:54:58 - PHP Warning: Cannot modify header information - headers already sent by (output started at ******/*******/******/catalog/language/norwegian/checkout/cart.php:1) in ******/*******/******/vqmod/vqcache/vq2-system_engine_controller.php on line 29

2013-07-03 7:07:03 - PHP Warning: Cannot modify header information - headers already sent by (output started at ******/*******/******/catalog/language/norwegian/checkout/cart.php:1) in ******/*******/******/vqmod/vqcache/vq2-system_engine_controller.php on line 28

2013-07-03 7:07:03 - PHP Warning: Cannot modify header information - headers already sent by (output started at ******/*******/******/catalog/language/norwegian/checkout/cart.php:1) in ******/*******/******/vqmod/vqcache/vq2-system_engine_controller.php on line 29

2013-07-03 7:07:34 - PHP Warning: Cannot modify header information - headers already sent by (output started at ******/*******/******/catalog/language/norwegian/checkout/cart.php:1) in ******/*******/******/vqmod/vqcache/vq2-system_engine_controller.php on line 28

2013-07-03 7:07:34 - PHP Warning: Cannot modify header information - headers already sent by (output started at ******/*******/******/catalog/language/norwegian/checkout/cart.php:1) in ******/*******/******/vqmod/vqcache/vq2-system_engine_controller.php on line 29

2013-07-04 1:36:55 - PHP Warning: unlink(******/*******/******/system/cache/cache.product.total.2.0.1.512022accdec061982311bce7dab7109.1372905374) [<a href='function.unlink'>function.unlink</a>]: No such file or directory in ******/*******/******/system/library/cache.php on line 45

2013-07-04 3:20:43 - PHP Warning: unlink(******/*******/******/system/cache/cache.product.total.2.0.1.512022accdec061982311bce7dab7109.1372911613) [<a href='function.unlink'>function.unlink</a>]: No such file or directory in ******/*******/******/system/library/cache.php on line 45

2013-07-04 5:36:20 - PHP Warning: unlink(******/*******/******/system/cache/cache.product.total.2.0.1.512022accdec061982311bce7dab7109.1372919681) [<a href='function.unlink'>function.unlink</a>]: No such file or directory in ******/*******/******/system/library/cache.php on line 45

2013-07-04 16:59:49 - PHP Warning: unlink(******/*******/******/system/cache/cache.product.total.2.0.1.512022accdec061982311bce7dab7109.1372960754) [<a href='function.unlink'>function.unlink</a>]: No such file or directory in ******/*******/******/system/library/cache.php on line 45

2013-07-04 18:26:41 - PHP Warning: array_key_exists() expects parameter 2 to be array, string given in ******/*******/******/catalog/controller/payment/bitpay.php on line 67

The first set of errors can be solved my disabling PHP notices on your server.

The second set of errors looks like it's trying to write to system/cache and either write permission is not setup correctly for the webserver user or the caching system cached some of your pages and the cache files that were generated are now deleted.