@elise, as to archival properties, liquid emulsion is really no fundamentally different from regular silver gelatin papers. The mechanisms of potential deterioration are the same. The physical makeup of the print does influence this, however.
The main issues you're combating against are:
1: Attack of the silver image itself by pollutants in the air or nearby materials (including the print/paper itself)
2: Deterioration of the gelatin binder
3: Degradation of the paper
As to (1), you can avoid most damage firstly by proper fixing and washing. Use a rapid fixer and an archival wash. The fact that you're using a very thin paper is to your advantage here; an archival wash procedure will be very effective. Make sure that the materials in direct contact with the print are intended for photographic archival purposes. Check with the manufacturer's documentation of the materials you use. This will also ensure protection against (3), assuming you're using a good-quality paper to begin with.
Since your print will effectively be exposed to the air as well as potential mechanical damage, the influence of e.g. sulfur compounds over time may be an issue. You could consider archival toning with selenium, gold or a modern variant of Sistan - although I'm always a bit skeptical about the supposed 'archivalness' of any toning that's not taken to completion. Still, it won't hurt. Sepia toning will work, too, but selenium and gold are a bit more subtle, color-wise.
Concerning (2), this is of course a bit of a challenge with the artwork being physically exposed. Storage/viewing conditions are the most relevant here; try to avoid overly high or very low humidity. Try to keep the print away from direct/intense UV light (esp direct sunlight); while this doesn't do much with the silver image as such, I suspect it can affect the gelatin.
Overall, as long as the print is treated as the delicate object it is, I don't expect major problems, to be honest.
I can't really help you with the first question, although I'd be inclined to just melt it at a higher temperature. I don't see how this will adversely affect the emulsion. Temperature control is very critical during production of the emulsion (esp. the process of ripening that controls silver halide particle growth), but that's handled by the manufacturer.