I heard that people can sign a truce with the brotherhood of steel instead of blowing up their base... But the elder don't even give the dialogue.

As far as I know if you dont destroy them then you have the legion and ncr on your ass. Thats what i did.

No if you complete the BoS missions then you get the dialog option from the elder and the BoS will fight with you and the ncr against legion

Which Brotherhood missions? The first one (find the scavenging parties and find the scouts), and the second (bug Black Mountain)? Is there another one after that? If so, did you complete it?

And who did you have in the Elder's chair? MacNamarra or that Paladin?

I got the Paladin in the chair.

My understanding is it dosent matter whos in the chair.The old elder comes around to reason once you do enough quests.

My basic understanding is the factions want you to either
A Eliminate the wild cards.
B Sign them up on your side.

Being a member of the brotherhood pretty much equals signing them up.Though its possible to do waaaay before you need to .

I already got power armor training, and there is no more quests.

Try getting that Brohood girl at the trade 188 spot next to Boulder City/Near the Dam [i believe]. She's a Brotherhood Scribe girl with the powerfist. I forgot her name. She has a full body robe with hood.

I'm currently doing her side quests where she's trying to get my help to convince the Brotherhood that they need to be more active in the outside rather than just hide or go kill people.
Could be a possible lead-off to an alliance between NCR and the Brotherhood.

Yes, you can. I did all the quests, joined the BoS, and when it came time to eliminate them, I told the elder that the NCR was looking to destroy them. Then he'll say offer a truce, and the NCR will take it.