That's a copper-plate engraving (or chalcography), the typical technique of the era. You'd etch lines (with a sharp-pointed tool) into a smooth copper plate where the black lines are to go. The plate is covered with ink which is then wiped off, leaving ink down in the recessed lines. Then paper is placed on top and pressed into the copper plate, and sucks up the ink where the lnes are. You can find videos like this one from reputable institutions showing how it was done. The older way was to do woodcut prints, which worked like a rubber stamp; the raised areas were inked. With engraving you could make finer lines, and it was somewhat easier. The downside is that since woodblocks work the same way as letter-type (which is also raised) you could print them together. Since engravings used a different method of printing they had to be done separately, so such prints would seldom be in-line with the text of books but printed on its own page (often at the back of a book). Otherwise you'd have to print the same page twice and get it all to line up (and indeed when prints do have lettertype printed on the same page, they're usually not perfectly lined up)

You can usually see a clear indentation and often some ink smudges from the edge of the plate, but it seems like there's some kind of mounting or matte around your image covering it.

The date the engraving was made doesn't really mean the print was necessarily made that year, just that it was that year at earliest. Plates don't go bad with time but they are only able to make a certain amount of prints. Experimentally, this could range up to 20,000 of them (K. L. Bowen and D. Imhof, "18,257 impressions from a plate," Print Quarterly 22, 265-278 (2005)) but most runs were surely far less than that. In any case it could be some decades later.

The principle of paper-making has not really changed, the main difference is the source of fiber; in the 19th century, mechanical and then chemical pulping was invented to make paper from wood fibers. Prior to that, other fiber sources were used such as hemp, linen/flax and cotton. This is probably linen. If you hold it up to the light, you'll see the laid lines (or wire lines), fine lines vertical with the paper and then thicker horizontal ones (chain lines). These are from these are marks from the sieve in which the paper is made. The paper may also have a water-market, which is from making a wire figure at the bottom of the sieve. (if there is a watermark, you can use it to identify the paper-maker - if you have the energy - which could help in dating it) You can still buy hand-made paper like this today, but it's expensive.

The main cause of paper turning yellow/brown with time is the reaction with air and light of the lignin in paper. Lignin is a big polymer compound that's in wood and which makes wood, 'woody' (that is, other plants don't have much if any lignin) Hence 18th century paper made from other fibers is often not as yellow as 19th century (or later) paper made from wood. (however there is today 'wood free' paper, which made from wood but where all the lignin has been removed)

In this case the matte or whatever the paper is on top of the actual print is obviously a lot more yellowed than the print itself. That's a sign it's made out of wood-pulp paper and it's a bit worrying, because acidic paper (which a lot of cheap wood paper is) browns and goes brittle and worse, will acidify and damage the print's paper. So you should remove and throw that out if it's not attached. If (horror) it's glued to the thing or attached in some other way you'd probably have to take it to a paper conservator and let them do it. You ought to store the thing between two pieces of acid-free buffered cardboard, which you can find at art supply shops and stuff. ('buffered' means its' got pH buffering so it's not just non-acidic, it'll help neutralize any acid it comes in contact with)

It's certainly fine to have on the wall, out of direct light. Provided they're framed properly and out of direct light (and not in a super hot and humid environment) they should not degrade significantly. Find a frame shop near you with experience with prints and art. It should be mounted with wood-free, acid-free and preferably buffered board and UV-protecting glass. (if you've gone to a good place they'll know this without saying but it doesn't hurt to verify)

Then you can write on the back of the frame where and when you got it. Not that that's necessary or anything but it's nice to know the provenance of things.