MO Theory: Why do hydrogen and lithium bond, but hydrogen and helium don't?
You've asked seemingly simple questions that get into quirky considerations. A molecule of HeH would very unstable:

$\ce{2HeH -&gt; 2He + H2}$

As Oscar points out HeH probably can be made. In all of deep space where molecules could go days before colliding with another particle there must be at least one molecule of HeH. So it can be "made" and it does "exist." But how would you detect it? 

Typically when we are talking about "making" something we are talking about making it in a earth bound laboratory. You make enough to at least observe it somehow. For instance a lot of radioisotopes have half-lives less than a second which really doesn't give an experimenter time to do any really "chemistry" with them. So in any practical sense the HeH molecule doesn't exist.