I asked + present/past tense

Solution 1:

5. I asked what his name is.
6. I asked where he lives.

These work fine. When I have asked someone a question recently, then I am comfortable using the present tense. I'll paint you a picture. My son and I go to the library. We see an acquaintance from a little bit of a distance. My son goes over to say hi. When he comes back, he excitedly reports, "I asked him what his name is, and you're not going to believe it, but it's the same as my brother so-and-so, only he spells it differently. And I asked him where he lives, and it turns out he lives right around the corner from us!"