I'm fairly new to woodworking, from what I can tell, finishes like lacquer are good for adding protection to wood and waterproofing them. The main issue I have with lacquer is the plastic-like gloss it has. Is it possible to stain something like pine wood to a darker colour, and then do something to it to protect it, whilst maintaining a matte finish with no/little gloss?
This area of "artificial-looking finishes" is fraught with the problem of individual taste and personal opinion and the finishes you think look artificial others would not.
And it is really not the gloss that is the issue with a finish looking "a bit plasticy" as many detractors express it, it's generally the thickness it is built up to. Almost nobody thinks a traditional French polishing job looks artificial even if left extremely glossy, and the reason is that the method produces this gloss with the thinnest build of finish possible (even a dozen layers may amount to less than one coat of varnish).
Is it possible to stain something like pine wood to a darker colour, and then do something to it to protect it, whilst maintaining a matte finish with no/little gloss?
In short yes, but there are some additional things you need to know about.
The first is that pine is notorious for staining poorly because it is a blotch-prone wood* (possibly the worst one there is unfortunately). And the darker the colour the more evident this blotching is.
As for a matt finish this is possible on any wood with any finish on it, so at least this part is easy.
Arguably the easiest way to achieve this is by using a purpose-made matt/matte varnish, but it can also be done by abrading a gloss finish to matt it down. Although it is more work the latter is my preferred way of doing it because it's more reliable, and it's cheaper. Matt varnish can give patchy results sometimes and you should ideally build the finish using gloss, then use matt only at the end, so you may need to buy two versions of the finish.
For more detail on rubbing a finish down see these previous Answers:
How can I reduce the gloss of a varnished piece of furniture?
Flat polyurethane finish for tabletop
*For this reason it is often recommended not to stain pine in the traditional manner at all but instead rely on coloured overcoats, e.g. "gel stain" (which despite its name is not stain, but a thickened version of coloured varnish).