I'm going to address the components of your question in reverse order.
There is a way to craft new shells, without a big apparatus, like in your own home?
Absolutely. You don't even really need power tools, although they help. The question is how LONG you can keep reloading the same brass until it doesn't work anymore. I've seen people state that they've been reloading .45 shells since the '80s without difficulty, as long as you're conservative with not putting more powder in than they were designed for.
Is it possible that this gun 'survives' (continue to function properly) for thousands of years without rusting or atomic decaying, using only the religious zealot-like care of the lineage of carriers?
The real problem is not so much atomic decay and rust, it's usage. A zealously maintained steel weapon surviving completely intact isn't only plausible, they exist today. There are swords in Japan that are said to be as much as 1500 years old and still basically look new. There are some cases of European swords almost as old that have been found in similar condition.
This is particularly true with firearms, since gunpowder puts a lot of force on the structure of the weapon. The biggest problem would be the rifling in the barrel, since there's just no way to keep that from being eroded over time as you use the weapon. There are also precision components like springs and so forth in the trigger mechanism that would be subject to failure over a really long period of time.
EDIT: Puppetsock provided a lovely link in the comments that puts some data against this. You're looking at ~5,000 rounds before the springs and so forth need replacement, and 50,000 rounds for the barrel. That sounds like a lot, but a weapon in regular use might see that much usage in just a few generations.
TLDR: For both the ammunition and the weapon itself, it's not how long the weapon is around, it's how often it's fired that's the critical factor.
If your idea is that there's a Navy Colt .45 that spends decades at a time in a gun safe being meticulously maintained and once a generation it's used to ceremonially execute someone, yeah, no problem at all. I have no doubt that some archaeologist in the year 5000 AD is going to run across someone's collection of AR15s in a sealed gun safe that's been buried in a flooded basement for three thousand years, and those guns will be as good as the day they were made.
If you're imagining something like the Gunslinger in Stephen King's Dark Tower where's he's putting literally hundreds of rounds through the thing on a regular basis, no way no how. The barrel would be dead in a couple decades, if not sooner.