What happens when I play Perched Grimwyrm while I haven’t conquered Dragon Roost this turn? Can I pay [A][A] and play it to Dragon Roost? What if I’ve conquered another battlefield this turn?

You cannot.

In Riftbound, “can’t” beats “can.” Perched Grimwyrm’s effect is a “can’t,” as in it can’t be played to any location but to a battlefield you’ve conquered this turn. Dragon Roost’s ability tries to give the Grimwyrm permission to be played to the Roost, but that can’t overcome Perched Grimwyrm’s own restriction. If you have no ability to play Perched Grimwyrm to Dragon Roost after paying for it, you will not be able to finalize Perched Grimwyrm at all. The actions taken as part of playing Perched Grimwyrm will be undone and it will be returned to the zone it was played from.

This is true even if you’ve conquered another battlefield this turn. If you have the ability, you can play Perched Grimwyrm to that battlefield without paying the additional cost of Dragon Roost, but you can’t play it to Dragon Roost itself unless you’ve conquered it.

Baron Nashor doesn’t work this way. He enters at the Baron Pit regardless of effects preventing him from being played to battlefields, because Baron Nashor’s passive ability generates a delayed replacement effect (“I enter there”) that replaces the event of him entering to any other location with him entering to the Baron Pit. That replacement effect gets around effects like Mageseeker Warden. Dragon Roost is not written as a replacement effect. It tells you where to play the dragon you’ve paid the additional cost for, but it doesn’t specify how that dragon enters the board. Therefore it is a permission on play location, but not a replacement effect.