Hey, welcome to the forum :). I suspect my answers to your questions will be fairly similar to those above, but here we go...
1.) Solo play - I have played solo a bit on Tabletop Sim but it is more work than playing with someone else since you have to run every deck, and while the game can have only one player, you still need at least three heroes. It's most common for me to play with one other person, who controls two hero decks while I play one. I always control the villain and environment decks as well but as that's more of a matter of just reading out card text it's not exactly super-complicated ;). If you ar trying to singularly wrap your head around all the hero decks in play whilst controlling the villain and environment decks at the same time, however (especially if one or more of your heroes is one of the more complicated ones), and especially if you're new to the game and therefore don't know the decks that well to begin with, it may get a bit much. But you never know, maybe you'll enjoy it :D. If you have Tabletop Sim you can download the game there (and/or play it with other people online, plenty of us are usually up for that :D), and there is also an official Steam version for sale by a company called Handelabra.
2.) Game/setup time - Setup is quick, just shuffle all the decks you're gonna be using, give the right number of starting hp to each target (I favour dice for this but there are tokens you can use that come with the game),make sure you've gone any "Setup" text on the villain's character card, and you're good to go :). Game length on average I would say is around half an hour, but I've had games lasting anywhere from around ten minutes to about three hours. Four if you include Oblivaeon but that's a super-big-mega-fight so doesn't really "count" alongside the regular games ;).
3.) Planning versus luck - There can be issues with "luck of the cards", and some heroes can be more affected than this than others, plus some villains have horrible cards that you may not be able to do anything about, but learning the decks, knowing what might come up, and getting the hang of various setups and combos that can help with it are all valid tactics. You could play a game with exactly the same decks multiple times and have a different game each time thanks to the randomness of card order, but depending on the exact decks used the game may be harder/easier. Some villains are just outright easier to beat than others (because they don't mess with your stuff so much or dish out loads of damage all at once), and some environments can help/hinder the heroes/villains depending on where you're fighting. I've played this game hundreds and hundreds of times by now and I'm not fed up with it - sometimes I get my arse kicked in minutes but there is no villain that I have never beaten at least once. It just takes more work with some of them, that's all ;).
4.) Teamwork/Combos - Can you combo? Ohhhhh, yes! This is a big part of what makes the game so cool, the working together to do stuff. I'm not even all that interested in the superhero genre but I frigging love this game :D. Certain heroes really really like certain other heroes because they let them do their stuff so much better, and some heroes are just good at making everyone better - it's not just about smashing stuff till it dies. Yes, some heroes are dedicated to that and if you didn't go smashing bad guys you'd never win, but some heroes are more focused on support and letting their allies do more stuff, or be better at doing whatever it is they were already doing. With some heroes you may never do any damage from that deck the entire game and yet still be amazingly effective. For example, there is one hero whose thing is constructing robots which do the majority of her damage for her, but she can't play them during the "play a card" phase of her turn. But if it's someone else's turn, it doesn't matter, which means she loves anyone who can give her an out-of-turn card play and get set up that much quicker. And then she munches everything to death with a mini-army of raptor bots :D. Figuring out new combos you can do is a big part of the game, as is learning different ways to play each deck - you might have a setup you prefer on one hero and which you always aim for, but then see that hero played by someone else a completely different way which works just as well as your way. The promos for each hero (alternate character cards with different starting hp and base power) also change up the way their decks are played. If you don't have these cards you can just find their info online and jot it down on a piece of paper or something, since it's not like character cards need to ever be shuffled into the deck or anything.
5.) Cool effects - Think I covered this somewhat above, but yes, there are plenty of things that aren't just "I hit it" :D. Even effects like that can spawn loads of other effects, depending on what's in play - "I hit it, which kills it", "Okay, this card the villain has in play means they get to play another card 'cause you killed their thing...okay it's a one-shot that hits you for X damage and stops you dealing damage for a round", "Nope, I redirect it so the villain hits that minion of theirs that was gonna murder us next turn >:)". That's just an example but you get the idea :D. Sometimes even hitting a fellow hero is a good thing! But outside of that, there is plenty you can do outside of hitting - giving heroes extra actions (play/power/draw), stopping bad guys dealing damage, looking at the top/bottom card of various decks, playing the top/bottom card of various decks, putting out your own bots/constructs/devices which do a variety of stuff on your behalf, etc. Each hero is different enough that while plenty of them can do very similar things (there are plenty of powers that are "Deal one target 2 <type> damage", for example), it doesn't feel like any deck is the same as any other because all the other stuff they can do, and the way it combos with the rest of their deck as well as those of their fellow heroes, can vary greatly. Even between games played with that same deck!
6.) I have played Ascension, but Sentinels isn't much like that - it's co-op, for starters ;). Some of the card things can be considered similar to the way Powers can work in Spirit Island, I suppose, with the "I'm gonna do X...no wait, hang on, if I do Y instead and you do Z, we can stop those guys from doing that thing they were gonna do and then get set up for later", that kind of thing.