Would or Could, in a list of questions, is the first verb always the correct choice?

Solution 1:

The answer to "is the first verb always the correct choice?" is No. The reason is the following:

If you choose "I wonder why and how someone could kill a person.", you're saying the same as "I wonder why someone could kill a person and how someone could kill a person." You don't mean that.

And if you choose "I wonder why and how someone would kill a person.", you're saying the same as "I wonder why someone would kill a person and how someone would kill a person." You don't mean exactly that either.

The only solution that I can think of is to rebuild the sentence, otherwise you won't be expressing what you mean clearly. Something like:

I wonder why someone would kill a person and also how someone could do it.