OR, he approves of the Quizzy helping others and being nice because that would be easier to get the Quizzy to help him or control. The best kind of manipulators are the ones you don't think capable.
He's also amazingly racist, think he could have stomached romancing other races?
Why would the writers go out of their way to make a false personality for him?
In-game, your Inquisitor has no way of knowing that doing things like that even makes him happy, unless he actually says so (and he doesn't always). He wouldn't become closer to you for doing things to help others, and further away from you when you are closed-minded/do things like recruit the Wardens, if he didn't really have honest-to-goodness emotions about those things, one way or another.
Solas is far from perfect. Yes, he's got some issues with the other races, too--but he's not "amazingly racist." He frowns on modern elves as much as he does everyone else. The problem is that, since he is from a couple thousand years ago, he knows the potential everyone has. And I think he's the one who caused that potential to become lesser (in his estimation) than what it once was. That's why he's so set on fixing it.
As for his plans... they are clearly dangerous, and that's why he doesn't want the Inquisitor involved. I'm not sure that he thinks the Inquisitor would disagree, necessarily--you've proven yourself open-minded and caring or you wouldn't have gotten his approval enough to be in a relationship with him in the first place. I think the problem is he might believe you actually want to help him, and that causes issues for him. For one, it's too dangerous for Lavellan. This is something he has to do alone. And also... whatever happens, he's probably going to have to give up on their relationship anyway. Maybe not even necessarily for Lavellan's safety, but because of whatever obligation or sacrifice he has to make to achieve his goals. Or maybe because he will have to help rebuild the elven empire and bumping bits with Lavellan isn't going to further that goal because she's not Elvhen the way his people were Elvhen, no matter how much he loves her.
We don't know.
As for romancing other races... if not for the need to deal with elven culture and vallaslin, I think he could have. For story reasons, it doesn't work. However, given time to become more open-minded about other races? Sure, he could have--the only possible reason not to being he simply doesn't want non-elf children, and I'd say that's actually pretty valid since we are learning there are quite a few things special about the elves as a race--things they've mostly lost. Just would not be possible in the scope of DA:I--he immediately was closer to an elf than anyone else. But, since he's probably never going to be a party member again, and since he has already been a romance in DA:I, that option will never open up no matter how comfortable he eventually becomes with the non-elves. He can be closed-minded about certain things, but he is always willing to admit when someone else has a point or when he is flat-out wrong about something.
Edit: And back to the topic of his goal...
We all tend to assume the worst about whatever it is he has planned, but we know that even if he is dropping the Veil, he's doing it in such a way that it won't be instantly catastrophic. He wants the Breach and the rifts to be closed--they harm people and they harm spirits. If he's waking the Forgotten Ones, well, as someone pointed out, Cole said they were hiding and hurting, not that they were angry and vengeful about being locked away.