about why trip was the father..
we do know just like soong for some reason paxton did know about trip and tpol. he even calls them "star crossed lovers " to trip in demon.
Yeah, I think Paxton even referred to them specifically as Romeo and Juliet in that speech. And one of his henchmen also taunted Trip about T'Pol and baby Elizabeth -- "You obviously did more than talk. And look at what you got for your trouble -- some half-human thing." So it certainly seemed that Paxton (and other Terra Primers) believed Trip and T'Pol were romantically involved and that was possibly a factor in the decision to use their DNA.
And from Paxton's POV, I can see why he would select Trip and T'Pol as "parents" -- assuming his goals were to undermine Starfleet's position and also give credibility to his claims about the dangers of interspecies mating.
He could potentially imapct both goals by selecting two high profile Starfleet officers whom he believed to be romantically involved and linking them to the existence of a Vulcan/Human baby. And even if Starfleet and/or Trip and T'Pol denied it, there would be enough "smoke" (the neuropressure, trip to Vulcan, etc.) to make some folks think there might be validity to some of the claims.
As to how Paxton came to find out about the T/T relationship, I tend to think it was from one of two sources (or possibly both). As others mentioned, it seems likely (based on Soong's comments) that there was a lot of post-Xindi media coverage about the crew, which presumably could have included speculation about the T/T relationship. Also, it's possible that Masaro passed on information re: rumors about T/T that were circulating on the ship. The existence of such rumors was mentioned a couple of times in S3 ("Raijin" and "Harbinger") and I think Malcolm also alluded to the rumor mill (re: T'Pol's divorce) in "United."