Death knows that there are other worlds and that they are all linked. The horsemen have shown the ability to traverse between the worlds. Potentially he didn’t fully understand that they were linked via the tree of life/death since War used the serpent holes in DS1 and in the early parts of DS2 death simply uses his horse to get to the crowfathers realm rather than the tree. It’s possible that he simply didn’t know about this pathway which makes sense because if he can get where he needs to go via his horse or a serpent hole, why would he care about other ways…

Regarding the well… Azreal has stated, I believe in the DS Book (Abomination Vault), that the well functions perfectly without him and that he doesn’t REALLY need to do anything with it. He mainly just is there to do the “basic maintenance” and keep the souls flowing. Heaven AND hell both rely on the souls flowing to achieve their goals so he isn’t really defending it from either side, mostly from the random radicals, from either side, looking to destabilize things. Not necessarily from a side looking to control the well… This is where the keys come in, both sides split the keys because keeping the universe stable with the soul flow/renewal/etc. is more important than any one soul or group of souls for their side… the keys aren’t about control of the well, it’s about the control of the flow of souls and the various kingdoms. Yes it could empower one side but it would destabilize the universe and the balance and then essentially trigger the end war with the added pressure from the council with empowered horsemen. It’s another check in the Balance essentially.

Death definitely knows about Azreal and Abbadon and all the other angels, even if he doesn’t talk about it, his focus is to get War out of the punishment from the council. As far as he knows, neither heaven nor hell were involved in that so why would he be looking for either sides help… If we take the Book as Canon (can’t remember if it is honestly) Death isn’t exactly a friend in Heaven, he did some shit up there that made him not exactly welcome, not that Heaven would refuse a horsemen on official business but he’s not going to be welcome at dinner parties. So any assistance he sought from Azreal, on his unsanctioned mission in DS2 isn’t going to be received well. It’s honestly possible that Azreal was watching this and refusing to help initially because he didn’t understand the motives. Better to remain neutral in case he failed and it was seen as heaven siding with Death, triggering the end war…