Yes, that sac is in trouble. My guess is that the pen was re-assembled without using talc to stop the latex from sticking to the inner barrel as it was inserted (and by the looks of it twisted while inserting).
I don't see a fill-lever - does it have one that's around the back of the photos, or isn't there one? If there's no lever there might be a hole drilled in the end of the barrel - you'd put the nib into a bottle of ink, then blow into the hole which would compress the sac inside the barrel forcing air out through the nib. Stop blowing and the empty space will fill up with ink. Best not to suck in case there's a pin-hole in the sac.
Sizes ... I'm going to check "Da Book" (officially "Fountain Pens - the complete guide to repair and restoration" by Frank Dubiel). He suggests one of 3 sizes fit pretty much everything - 12, 16 and 20. Those indicate the diameter of the mouth - which you want to be a snug (but not tight) fit on the nipple. Use fresh Sac Cement (shellac) to seal the mouth against the nipple.
But first trim the length so the sac doesn't hit the bottom of the barrel cavity when it's pushed in there. (That would cause ink to be squirted out under pressure.)
Buying a replacement sac (and talc, and sac cement): the place I bought from seems to be out of business now, it was
www.fountainpensacs.com but there's another
The Pen Sac Company (might be the same operator for all I know). Their guide suggests "20 straight" for a hard rubber Esterbrook (which this looks like to me)
Edit - looking again I think I misjudged, it appears to be plastic not hard rubber ... probably be smart to buy a couple of each size 16 and size 20, they are only a couple of dollars apeice.
Edit #2 - Frank Dubiel says that nail polish is an excellent substitute for sac cement, the important thing is the nipple must be clean and smooth and completely coated to make a 100% seal
View attachment 380384
They don't appear to sell talc or sac cement - but maybe if you contact them they'll be able to point you in the right direction.
Duncan