This is Diane Duane's Young Wizards series. The main characters are Kit and Nita, who get roped into becoming wizards, people empowered by The Powers That Be to fight against the Lone Power, who embodies entropy.
Boy somehow ends up in a mirror universe that's darker and seems to have no people. He has to travel to a certain office(?) building and steal a book. I think this is towards the end of the book (I can't remember the events leading up to it). I think he finds the portal in a forest or something behind his school.
So You Want to be a Wizard - Kit and Nina travel to an alternate world where the Lone Power reigns to steal "The Book of Night with Moon" and relight the sun.
He goes into the ocean with mermaids or something and has to save the ocean from pollution.
I think you're referring to Deep Wizardry, where Kit and Nina travel with whales. It's a magical ritual, though.
Aliens exist and are observing Earth, because they think it's undeveloped and are waiting for them to be advanced enough.
Aliens show up in several books in the series, so I'm not entirely sure on this one.
His mother ends up in hospital and he does something to save her.
He goes to Ireland(?) and enters a mountain or something to find a race of people. I can't remember who showed him how, but I'm pretty sure she used magic.
He goes to Mars and saves a race from war with themselves(?). This place was hidden inside an illusion. He's also grouped with a linguist that learned their language.
Possible A Wizard of Mars. I haven't read that one yet. I vaguely recall Wizard's Holiday involving an illusion on another world, but it's been a while.
He travels to another world where there's a prince. I can't remember, but I think it might've been part of a tournament.
Sorry. No clue on that one.
His sister goes to a robot planet through a portal. I think the actual planet was a robot/AI and had lots of little robots on it. Can't remember what happens here, but he goes there and saves her from something.
High Wizardry. It's actually Nita's little sister, Dairine.
It was set a few years ago, when computers weren't common (his family got one early in the first book, I think).
It's a running joke among fans of the series to point out that the technology advances incredibly fast in-series, as the third book introduces the spell computer as a state-of-the-art Apple computer (with no bite out of the apple on the logo) that's recognizable as 1980s technology, and the current books have spellbooks on iPods, all apparently in the space of a few years in-universe.