Fix 502 Magento error in front end and 4001 deadlock in admin.

I have a problem with my Magento shop. The problem appears only when some one working in admin (add/edit a product). In admin I receive an error ( SQLSTATE[40001]: Serialization failure: 1213 Deadlock found when trying to get lock; try restarting transaction). 
Even the indexes are set to manual and I am using an extension for asynchrony re-index. The customers received an error (502 Bad Gateway) in the front end. After the 502 error the site can not be open from the customer until clear all browser’s cookies. Also I have MySql slow queries which also can cause the problem. I tried the most popular methods for serialization like few tries and etc. I will pay only if the problem is completely fixed. Errors log for nginx: 2015/04/15 12:32:38 [error] 20009#0: *5006364 recv() failed (104: Connection res et by peer) while reading response header from upstream, client: [login to view URL], server: [login to view URL], request: "GET /checkout/cart/ HTTP/1.1", upstream: "fastcgi://u nix:/tmp/[login to view URL]:", host: “[login to view URL]” 2015/04/15 12:31:57 [error] 20013#0: *5006127 recv() failed (104: Connection res et by peer) while reading response header from upstream, client: [login to view URL], server: [login to view URL], request: "GET /ajaxcontent/homepage?tabType=mostSelled HTTP/1.1 ", upstream: "fastcgi://unix:/tmp/[login to view URL]:", host: "[login to view URL]", referrer: "ht tp://[login to view URL]“ 2015/04/15 12:24:17 [error] 20009#0: *5003825 recv() failed (104: Connection res et by peer) while reading response header from upstream, client: [login to view URL], server: [login to view URL], request: "POST /checkout/onepage/saveBilling/ HTTP/1.1", upstre am: "fastcgi://unix:/tmp/[login to view URL]:", host: "[login to view URL]", referrer: "http://xxxx. xxx/checkout/onepage/“ 2015/04/15 12:19:19 [error] 20005#0: *5002826 recv() failed (104: Connection res et by peer) while reading response header from upstream, client: [login to view URL], server: [login to view URL], request: "GET / HTTP/1.1", upstream: "fastcgi://unix:/tmp/php5- [login to view URL]:", host: “[login to view URL]” 2015/04/15 12:07:20 [error] 20012#0: *4997912 recv() failed (104: Connection res et by peer) while reading response header from upstream, client: [login to view URL], server: [login to view URL], request: "GET / HTTP/1.1", upstream: "fastcgi://unix:/tmp/php5- [login to view URL]:", host: "[login to view URL]", referrer: “[login to view URL]“ 2015/04/15 11:39:57 [error] 20006#0: *4983814 recv() failed (104: Connection res et by peer) while reading response header from upstream, client: [login to view URL], server: [login to view URL], request: "POST /checkout/onepage/saveShippingMethod/ HTTP/1.1", upstream: "fastcgi://unix:/tmp/[login to view URL]:", host: "[login to view URL]", referrer: "http ://[login to view URL]“ 2015/04/15 11:38:33 [error] 20012#0: *4984030 recv() failed (104: Connection res et by peer) while reading response header from upstream, client: [login to view URL], server: [login to view URL], request: "GET /checkout/onepage/progress/?toStep=shipping_metho d HTTP/1.1", upstream: "fastcgi://unix:/tmp/[login to view URL]:", host: "[login to view URL]", ref errer: “[login to view URL]" 2015/04/15 11:37:08 [error] 20012#0: *4984032 recv() failed (104: Connection res et by peer) while reading response header from upstream, client: [login to view URL], server: [login to view URL], request: "GET //fcheckoutpromo/checkoutpromo/ajaxCheckout/ HTTP /1.1", upstream: "fastcgi://unix:/tmp/[login to view URL]:", host: "[login to view URL]", referrer: "[login to view URL]"