The Borg have been retconned from the beginning. Originally they were meant to be insectoid aliens, but then that was changed due to budgetary restraints to humanoids with cybernetic enhancements. In the episode where the Enterprise first encounters the Borg they do not attempt any assimilation of humans, and that attribute is only added in later episodes. So the Borg have assimilated new attributes throughout history, with First Contact continuing that noble tradition.
As for time travel, there is almost no story where it makes sense so it’s not a big deal to me. I imagine that the Borg would rather not resort to time travel themselves for just these paradoxical reasons, but when they are at risk of being destroyed why not?
Picard’s strange characterization is probably the worst part of the movie from a continuity perspective, but you’re going to set yourself up for disappointment if you expect any of the Star Trek movies to be particularly true to the TV shows. I view First Contact largely in isolation, and in that way it succeeds brilliantly. Kind of like TLJ actually. It’s when you try and reconcile it with the larger story that the issues appear.