Will Installation of Service Pack 3 on SQL Server 2012 Web Edition (existing production) require database restore activity?
Installing service packs usually goes like this: detailed step by step guide


It shouldn't affect databases, but you may want to test installing SP3 on the test server first. It will help you get an idea how long it takes (management will want to know that beforehand). It will also give you a chance to find out if any of your applications (or anything else) got affected. Safety always comes first so production is never the best place to patch first. 
No, you don't need to restore anything. Existing databses will be in the same state as they were before the installation. Settings (collation etc) will remail unchanged as well.
You may want to read about bugs in SP3 and potential problems that can occur during instalation. There is plenty of examples on Google. You may also want to kave a look at the release notes to understand better what fixes are contained in SP3.
I always do (just in case), but you don't have to. It is really about how concerned your managers are about data integrity, safety etc. It is usually recommended to backup all databases before any maintenance.