Did Wilson have a past relationship with Elaine?

No. He met her when he came to the US to kill Valentine.

No. Although I think the relationship that emerged between Elaine and Wilson was a little odd. On one hand, she's one of the few characters who is routinely critical, often harshly, of Wilson. She has her life together, including a kind of lucrative job with Hollywood productions.

Yet she really lets Wilson, who is obviously a driven character bent on revenge, into her life and contributes in some way to his mission against Valentine.

I think in a lot of ways they could have dropped the Guzman character entirely if Elaine (Wilson's daughter's "best friend") had written the letter attributed to Guzman. Guzman's only real narrative development was being Wilson's driver and arranging the gun buy from the cholos in the park. Elaine could have been the driver, and Wilson could have had a neat scene of cultural mismatch buying the gun in the park on his own -- using his cockney moxie to get the confidence of the gang guys to sell him a gun.

This would have given Elaine's relationship with Wilson more substance and depth.