I know some but not all, please help lol

So I have a 97 jeep Cherokee SE 4.0 and I've worked on cars so I'm fairly knowledgable on engine but I'm quite dumbfounded by this:




It is the rubber tube that has a chunk of it ripped or cut out by the u joint on the axle. I followed it to the second pic where it goes no where and is capped and followed it to the third and fourth pic where it ends in to the diff housing on the axle????? What the heck is it? Was it an old tube to the older vacuum axles? Any insight would help.
Second question is the throttle and brake booster dealio, I read it somewhere, can't find it and I pushed on the brake multiple times and you could hear the rpm move up and down, now I know the tube is suppose to hold a vacuum to it but when I looked at the tube connecting the brake booster to the manifold, it has the tube in it but with no clamps, would that be the cause and issue? Is it just an easy fix of clamping the tube down on the ends or is there more to it? Insight and answers would greatly help

it's the diff vent tube. just make sure it's continuous up to the little breather so it doesn't suck water from puddles and don't worry about it.

there are no clamps on vacuum tubes. some RPM fluctuation is normal.

Should I get a new hose then? Because its got a good size chunk missing as the pic shows from it rubbing on the joint of the axle. And define little fluctuation please lol

yes to avoid water from entering the diff.

Zip tie the vent tube to the LCA to keep it away from the DS.

JIM.