Am I running a 32-bit or 64 bit Sql Server

I'm getting:

Microsoft SQL Server 2012 (SP1) - 11.0.3128.0 (X64) 

So yes - X86 means 32-bit, and in my case, X64 stands for 64 bit

and exec master.dbo.xp_msver returns:

4   Platform    NULL    NT x64

Again - x64 = 64-bit, while yours says X86 = 32-bit

This: Microsoft SQL Server 2008 R2 (SP2) - 10.50.4000.0 (Intel X86) means you're running the 32-bit (X86) version.