Boii became a horde and now have 7 full stacks, not 3

As Lugiones, I captured the last Boii city and they became a horde. Suddenly they have surpassed Rome in military strength (behind only the Seleucids and Ptolemids) and are besieging my towns.

Late in the game I could perhaps handle this, but at turn 75 I can scarcely maintain two stacks.

Will they keep all these troops once they resettle?

No there's a random chance within the code that a certain amount of their troops will be lost.

Also- due to the fact that professional full time armies were rather rare in that era- it's no surprise you can only manage 2 stacks as the human player.

AI factions get scripted aid with money, otherwise they'd all go bankrupt and totally passive within a few turns. The human player doesn't get any such assistance.