(1a) This doesn't work in this case, because the cold is finished so he must have recovered. The logic does not permit the mixture of tenses. You could easily say, 'He had a traffic accident, and hasn't recovered yet'.
(1b) For good form, drop the second 'he' as unnecessary.
(2) Both OK.
(3) Both OK, but (3a) would be less common (I have a little trouble with this one because I am not British, but Canadian American, and this form is more common in BrE; so it sounds a little awkward to me. I would say, 'have gotten'.)
Student or Learner