Can I get my allies' plaques?

Use your enemies

This might be a little dirty but I've done it a few times and it does have a certain chance of failure.

The base idea is to lure your enemy to attack that town which you want and then take it back before your ally send their army to do so.

It will be easier if your ally is of a different allegiance since you can corrupt or purify their land to make it weaker or even overrun it with rebels which can be easily taken down by yourself. But since you are Lizardmen with High elves and Dwarfs allies... you need to put in more effort and resources to do so.

Chaos unexpectedly is your best "Friend" here. They are roving, likes to leave town in ruins and spawns in large amount. What you need is an army strong enough that they do not dare fight against head on and push them towards the town you want. Give them some breathing space once they are near enough and they'll raze the town(most likely). The penalty is that you'll have to build the town from scratch(Level 0) and it will be chaos corrupted when you take it over. Also that the Chaos army might potentially be right in the middle of your alliance territory and therefore cause more damage than you'd liked it to after you are done.

If you are lucky, sometimes there might be unexpected opportune enemies. If your ally recently taken a plaque producing town and it is right beside a neutral faction that can win you ally in combat. It might be worth the risk declaring war with that faction and let them take that town before you march in and take it from them by force. The downside of this of course, is that you'd have another enemy to deal with. This can be a very valid tactic if you currently have no active wars. It gives you a new target to use your army against while gaining you a strategically important location.

No, there is not. Province trading was removed a while ago. I think either in Rome 2 or Shogun 2. You have to conquer provinces militarily.

But as I always say: do not bother with alliances in Warhammer: Total War unless you can confederate that ally at some point. It's more trouble than its worth.