Actually ... only the last one sounds reasonably natural, while the first one could be OK, too. Looking just at the first part of the sentence, it would most often be expressed as: (a) "She will do whatever he tells her ..." , OR, (b) "She will do whatever he tells her to do ..." I've done a quick google search and it looks like the second one (b) might be a little more common, but it's pretty close. Your version: (c) "She will do whatever he tells her to ..." can be seen also, but not as often as versions (a) or (b), I believe. Plus you are ending the clause with an infinitive, which is not strictly the best grammatical form. As for the endings, in #2 the phrase is usually "... second thoughts" (plural). In #3, you can say "... without any second guessing." (Drop the "it" or "him".) So if I was writing this sentence, it would be one of two ways: "She will do whatever he tells her to do, without any second thoughts." "She will do whatever he tells her to do, without any hesitation." Drop the "to do" from either one and they still sound natural. Also, note the addition of a comma which I think marks a natural break between the two things being expressed--what she will do and how she will do it.

Yes, fairly natural.