http://msdn.microsoft.com/en-us/library/x0w2664k.aspx
1) Allways check msdn first. Mixed mode means that the assembly can run managed and unmanaged code.
2) Setups for 32-bit Windows (.NET Framework 4.0)
http://system.data.sqlite.org/sqlite-netFx40-setup-bundle-x86-2010-1.0.74.0.exe
You kinda answered that question yourself “My project that is going to use this library is all .NET 4 which will be compiled to x86.”