Aha! Pictures definitely help. So let's talk about this one component at a time
Your slide is all nickel slide. (Bach slides that are lightweight (LT42) are also made of a nickel-brass alloy, without oversleeves). The problem with nickel is that many people are allergic to it. Your cork barrel is pitted as is the part of the slide that you would normally hold. However, the pitting is not very bad and if you are not allergic to nickel then you'd have no problems. If you wanted, you could have a tech relacquer it. It would be expensive, but at least your hand would not be touching metal.
Another common technique that is used - but one that you have to be careful about - is using fingernail polish. Yes, fingernail polish! They make an assortment of colors, including clear that can be applied. The reason you have to use caution is you want to make sure you don't seal in the stuff that is causing it to be pitted! Since the horn is older, it probably needs a chem clean before you do this. This really should be done professionally unless you really know what you are doing with chemicals. More on this a little later.
Note: This is a lot thicker than lacquer, but your hand is already gripping the area so it isn't likely that you'll notice this sonically. And, worst case scenario if you do, you can remove it easily.
** Bell **
I'm really not in a position to identify red rot, but clearly there is some corrosion going on here. Brass does not rust, but it does dezincify. As with the slide, the horn is probably long overdue for a chem clean. I'd get that done before anything else. You can figure out what to do from there. Nothing stops the process of red rot (if this is indeed red rot) once it is started. Even lacquering. You just have to replace the part eventually.
Once you get a chem clean on the bell, you can possibly choose to leave it as-is or buff it out. Its hard to say prior to doing the chem clean. I would personally go the route of having the lacquer removed and the bell buffed. A slight deviation from this would be to have a satin finish applied. I have done this to several of my own trombones with a bench grinder and a steel wool wheel. You will still want to get the chem clean prior to this, but you can save on labor cost if you do the finishing yourself. The advantage of having the lacquer removed is that you may maintain the bell yourself with brass polish. It also won't get anything trapped under the lacquer so it may actually require less maintenance.
There is also a contingent of players who find that lacquer has a detrimental influence on the sound, especially on the bell. You may find that if the lacquer is removed, that the horn plays much better than it did with the lacquer.
Finally, you can get the horn re-lacquered. This is purely optional though and largely for aesthetics. There is a marginal amount of protection it affords the brass under it, but it needs to be wiped down frequently just as raw brass would or else you will end up with a horn that looks like the one you currently have!
What I would do is have it chemically cleaned in addition to what I recommended in your other question and remove the lacquer from the bell. But what you choose to do may be different depending on your preferences.