Is it possible to have a liberal attitude toward sex and be opposed to abortion?

Why not? Though I'm not exactly sure what you have in mind about having a liberal attitude toward sex, I can imagine having permissive views about sex among consenting adults -- views that permit sex outside of wedlock, sex outside of stable monogamous relationships, kinky sex, etc -- and thinking that abortion is generally impermissible except in limited cases involving such things as rape, incest, genetic deformity, or the health of the mother. One might have the liberal view about sex, perhaps because one values individual autonomy. But one might think that responsibility goes with autonomy, making one responsible for one's autonomous choices and their reasonably foreseeable consequences. In this way, one could combine a kind of liberal view about sex with support for some restrictions on the permissibility of abortion. I am not endorsing this combination of views, but I don't see that it need be unprincipled.

Is it ethically and morally wrong to have sex with someone other than your husband for procreation purposes (if they are aware of it)? Especially when your husband is sterile and asks/gives you permission to?

This is a traditional solution to your problem, one resorted to more often prior to the advent of in vitro fertilization. I'm not sure that there is anything wrong, as such, with having sex with someone other than your husband for purposes of procreation when your husband is sterile and provided all three parties (you, your husband, and the other man) fully understand what you're getting into and fully consent to this arrangement. It's not clear from what you say whether your husband would know the identity of the other man, though I'm assuming he would. Having said this need not be impermissible, there might still be lots of reasons to wonder if it was such a good idea. Any one of the three of you might end up uncomfortable with the idea that you had sex with someone other than your husband, even if it was ostensibly for this limited biological purpose. Moreover, pregnancy doesn't always result from a single act of sex. Are all three of you prepared for multiple sexual episodes if this is necessary...

Is prostitution wrong? Clearly, it's illegal in some countries. But is it really immoral or wrong? Surely prostitution may, in some limited set of cases at least, even maximize average utility, or involve consenting adults who agree to being used by one another, or one by the other, as "mere" means. What is the relevant difference, in principle, between a one night stand and an instance of prostitution? Or between paying for sex and paying for a cab-ride home for one's sex-partner after a one night stand (or paying for a meal or drinks beforehand)?

It's hard to believe that prostitution, as such, is wrong. There would seem to be cases in which this could be an unobjectionable voluntary exchange of services in which both parties are free to make the exchange. In such cases, it's not clear why engaging (or serving as) a prostitute would be any more objectionable than engaging (or serving as) a massage therapist. If so, there could be morally permissible cases of prostitution. But, of course, many cases are not like this. In many places in the world, many prostitutes are forced into sexual slavery, against their will, at a young age. Even where prostitutes were not forced by others into prostitution, many choose prostitution out of economic necessity, as someone might choose to sell a kidney out of economic necessity. Many who choose prostitution find themslves working for pimps that are abusive and don't allow easy exit from the profession. In conditions such as these, the sellers of sex may not be acting freely or, if freely, with a fair...