Both of you sentences are usually undertood to mean the same thing, however I think there is a subtle difference.
I will try to answer any questions you ask.
means what it says, the expected outcome is an answer.
I will try and answer any questions you ask.
is slightly different, since an explanation may usually be given for the train of thought in trying to arrive at an answer, though the final answer may not be revealed at the end.
Consider the difference between
Let's try to see how we can agree on this.
Let's try and see how we can agree on this.
The former objective is reaching agreement, the latter is more a negotiation to explore how agreement can be met.