RIGHT, so where to start.
So, nations are pansexual, for the most part. Their morals are vastly different from those of people because of their long lifespans and because simply, they are not people. Primarily, they have to be pansexual for the sake of their people. I do subscribe to the idea that some nations do engage in sex once a treaty is signed to help firm up the pact between the two nations. This is not mandatory in any sense, and of course, it has to be consensual. This is how, I imagine, characters like Italy and Germany can be virgins for so long and it be believable in my eyes. (In that same vein, I also do not believe that they are... I guess true virgins? Virginity, like sexuality and gender, is a tricky thing to determine. Do you lose your virginity from a hand job? Oral sex? Italy and Germany are virgins in the sense that... it did not get put in. They've done other sexual acts, just not vaginal or anal.)
Moving along, nations do have sexual preferences because it just goes along with their personality. I'll be using Spain and Turkey as examples for this since I know them the best. Spain, if he was just a human and not a nation, I see as someone being bi/pansexual. He is someone to not care for a person's gender and would love them for who they are. Spain's type would just be anyone he enjoys spending time with and who are adorable in some way, shape or form. He would have an equal amount of boyfriends and girlfriends, all of them longterm and all of them splitting amicably. A few flings here and there when he's single, but otherwise, he's a relationship kinda guy.
Turkey, on the other hand, is someone I would see as being primarily heterosexual, but would have no problems with men if they were interesting. Even then, Turkey has a specific type he would fall for. He likes women that he has to fight to get in some way. Whether he has to fight someone to get them, fight them so they reciprocate his feelings, or just plain fight with them even if they are already together. Fact of the matter is that Turkey likes women who top and don't roll over at the sign of conflict. He would have a lot of flings and one night stands, mostly with women but with some men here and there, with a few long term relationships that mostly end on bad terms.
Though, one thing they both have in common, and that being is they both have a lot of sex. Spain would see sex as being the most passionate expression of a couple's love for each other. It'll be something that he wants both him and his partner to enjoy. Turkey, on the other hand, finds sex as one way to compete. Turkey loves to win, and the bedroom just becomes another battleground. He honestly enjoys it, but the competition center of his brain is something that is hard to turn off.
... wow, this spread into a tangent, but the point I'm making is that yes, nations have preferences, in spite of being pansexual. I can see Iceland and China as being asexual, France as being pansexual, Sweden as being primarily homosexual, Austria as being primarily heterosexual, etc.
As to fertility, no, I don't think nations are capable of having babies. Firstly, I do see relationships between nation and person as something that happen from time to time. They are not common, mainly for the reason that since nations do not age and have long lifespans, at some point, the relationship will have to end due to the human getting older. A nation and human having a child is something that I do not see as being possible. These are two different beings, in spite of their appearances. Secondly, familial relationships between nations are more of a metaphor for the relationships than actually being bilolocially related.
Nations are the constructs of their people! This is something that I've always believed in since I first joined the Hetalia fandom almost... wow two, three years ago. A nation comes into being when a group of people find themselves identifying as being of that nationality for the first time or when the idea of that nation is first conceived, essentially (which is why I believe there is a Catalonia and a Basque tan in regards to Spain). They grow physically in accordance with the growth of their people and nation. A nation dies when it's people die or no longer believe in it. The idea of a nation getting pregnant is one I find hard to believe, for the same reasons said above! The power of ideas and thoughts make it extremely difficult for a "mother nation" to come to being. Nations recognize when another one is similar to them and form relationships from there!
The Romance family call themselves brothers/sisters because they were all under Rome. Both halves of Italy call Rome their grandfather because Rome is a precursor to modern Italy, which only came into being following Italian unification in the 19th century. In a sense, Rome is the father to the "Italy" that came into being following his fall, who in turned "fathered" Romano and Veneziano. I'm using the terms just to have something to put. "Italy" would be all the Italian nation states that existed prior to Italian unification. AND WHILE WE'RE ON THE SUBJECT OF ITALY.
Yes, they are two because of the sharp cultural divide between the two. Northern Italians and Southern Italians view themselves has being two separate countries. There is even a movement in the North where they wish to separate into two separate countries again. But because they represent Italy as a whole, they call each other brothers and even if they were not one country, they'd still call each other brothers because their people all call themselves "Italian".
Now onto the idea of swapping gender. This is actually an interesting idea about the nations being sexless and are capable of swapping genders. That is honestly something I have not thought of and can understand the thought process behind. Though, I do not think that they can swap between male and female forms because they wish to. To me, a change in gender would probably only take place during a rebirth, like what happened with Greece. Ancient Greece was female, modern Greece is male, and should Greece die and be reborn again, I imagine that the Greece version III would either be male or female. It's just a flip of the coin really on how things happen.