I think I did the flirt thingy, but what is the "collect artifacts" part? Does that come after "Wicked Hearts"? I haven't done that one yet- still doing all the War Table stuff post-"Abyss." I haven't gotten much of a romance-feel from Solas yet, while Blackwall was already up for a kissing scene before "Abyss." (I'm avoiding the latter to prevent it...)
For flirting: To be sure, here's the "flirt" option when you first talk to Solas in Haven.
For approval: In general, Solas is incredibly easy to raise approval with. Ask lots of questions, because he approves of nearly every one. Bring him with you when you help people in the Hinterlands, as he gives more approval than perhaps any other companion for small acts of kindness (except maybe Cole and Sera).
You've also received Solas' first quest, Measuring the Veil, where you seek out an old elven ruin northeast of the Crossroads in the Hinterlands to activate an elven artifact, yes? There are dozens of other elven artifacts scattered all over Thedas, and Solas gives slight approval when you light each one. Then there's All New, Faded For Her, which nets a good amount of approval if you're kind, supportive, and helpful toward Solas and his spirit friend instead of a jerk.
In general too, there is no "deal-breaker" for Solas, except being a jerk to him and his spirit friend in All New, Faded For Her. As long as you don't constantly put down his friend for being a "demon" or make it clear that you only care about the mages or prefer to kill his friend, generally you can do anything Solas disapproves of and he'll still forgive and like you (and love you), provided it doesn't all add up.
In my first playthrough, I did a number of things Solas didn't approve of; didn't let him kill the mages in his personal quest, made Cole more human-like, and spared the Wardens, but he still loved me because I did other things he liked to balance it out. (Asked lots of questions, showed open-mindedness toward spirits and the Fade, helped people, helped mages and elves, etc.)
On Romance: Yes, Solas' romance doesn't all happen all at once. It's carefully spaced out over the course of the game, and Solas himself has... commitment issues, so you have to be patient and understanding. I think it's worth it in the end though. 