That doesn't really answer my question: why did the Horadim pick an old, abandoned cathedral to hide Diablo's soulstone?
Well, your question was "How did Diablo end up in Tristram's Cathedral?" But to answer this question, the Horadrim did not pick an old abandoned Cathedral. They picked a spot that they deemed 'safe' by some measure, and then built the Cathedral around it to protect and hide the soulstone.
Also, since Tyrael knew about the Hellforge, why didn't he and the Horadrim take the Soulstones there to have them destroyed? Even if he didn't know about Izual's treachery, why would he be content with keeping the Prime Evils imprisoned?
There is no official answer as far as I know, but to the best of my knowledge, it was out of naivete. This was the first time Heaven had attempted to use the stones, so he probably had no idea what would happen if they were destroyed. However, he assumed that hiding them forever would work. As seen in the Wrath animation, the Angiris Council is king of big on imprisonment. However, when it became clear that imprisonment within the stones was not an option, destruction was plan B.
I was under the impression Diablo required a body to be able to manifest himself as the big red horny demon we all know. He's not Belial and he doesn't seem to be able to conceal its demonic nature: the Dark Wanderer, once utterly taken over by Diablo, didn't look all that human and possessed Leah wouldn't have fooled anyone either. This is why I don't understand why it had to be specifically Leoric.
It was a dual reason. Firstly, Leoric was deemed to be the strongest soul in Tristram, and so he was targeted. Secondly, he was a powerful man with an army, so exploiting that for evil pleasured Diablo.
It strikes me as odd for a being supposedly as calculating as Diablo to pick an infant - let alone, Leoric - to be his host. Is it because Albretch's royal blood or something? If not, why not attempt to possess Leoric again once he has been driven completely mad?
Albrecht was by no means an infant. I don't know if his age was ever officially stated anywhere, but I'd estimate he was 10 - 14 years old when he was darkened. It did have to do with his bloodline, though. Even though he couldn't directly control Leoric, ruining his life and mental state cost many lives in Tristram, as well as in the armies of Westmarch and Khanduras, which again, is something that gets Diablo's jollys off.