A question of desire

Hope that got your attention
I know that base2+tai is for me or for questions, and base2+tagaru is for others. My questions are:
1) Do I use tagaru, or do I use tagatteiru (or either, depending on the situation)?
2) Instead of tagaru, can I use tai + omou (or omotteiru)?
3) If any of the above that are correct, is there a difference in meaning or nuance?
Thanks for the help!

According to the dictionary,

２ そのように振る舞う、そのようなふりをする、の意を表す。「偉―・る」「得意―・る」
Expresses that (someone) acts in a certain way or acts a certain way. "To act important." "To act like an expert."

Putting that with the explanation I remember being given by teachers, -tagaru would mean that someone acts in such a way or shows outward signs of wanting to do something. I think most commonly it would be -tagatteiru, because that shows an ongoing state as opposed to a momentary one. You can use it to show that someone has shown that they've wanted to do something for a while now, or was doing it the last time you saw them, whereas -tagaru would be more like they're showing it right at this moment.

Because of those qualities of -tagaru, I think you'd be hard-pressed to use it when someone just said they want to do something, brought it up in passing, or whatever. In those cases -tai to omotteiru or -tai to itteiru would have to be used.

I was going to look this up in whichever Dictionary of Japanese Grammar covers it to be sure, but I just remembered they're a few states away at the moment, so I'm mostly going off of memory here.

As Glenn-san wrote, "-tai to omotteiru" is used for the speaker.

"-Tai to omou" is more likely an expression of the speaker's determination.

thank you