Why even have another Eve?

What do you mean "another" EVE? They only made one of her cloned from the original hybrid SIL. As for why they felt the need to create her I figure that the military didn't see death by fire as a fool proof method of extermination so they cloned her as a gineau pig to develop a more reliable solution. Lastly i dunno where you got the idea that her mating with patrick was ever part of the plan. I mean they spend most of movie trying to keep them apart specifically to prevent that from happening lol. The whole telepathic link and mating angle made no sense to me either tho. IIRC the signal picked up by SETI that contained the "recipe" that created SIL originated from the vicinity of the star Vega so i don't see how there was any relation to a second alien that laid dormant on Mars. I guess one could assume that if there was life on mars at some point they could have fallen for same trick we did and the creature they made went dormant after it wiped out the martians until it got picked up by the astronauts.

They didn't clone Sil. In Species, they explained that many "Sils" were made - most didn't survive - and two spares were frozen (obviously a setup for a possible sequel). Eve then was more accurately Sil's twin. In Species III, Sara is referred to as a "third generation". As Eve's daughter, Sara would be "second generation".