What are the advantages/disadvantages of different methods of attaching handle to a knife (burning, gluing and pinning)?

I have no knowledge of “burning”, but . . .
I have never considered doing anything other than gluing and pinning. This is mostly because I like the look of pinned handles. Adhesive alone will work well if you are skilled and use a superior product such as Acraglass (for example).
Also, I consider adhesive a must for any non-folding knife, because NOT bonding invites the intrusion of environmental particulates, including bacteria, and this is especially critical for kitchen knives. You do not want bacteria trapped in your knife handle.
Another problem that I have seen with non-bonded handles, is that having your knife in a watery environment such as outdoors or even washing them at the sink, can lead to your handle material bowing away from the tang except where the pins are, even with stabilized wood.
Even if you bond your handles, really bad handle warping and pull away is all but unavoidable if you put your knife in a dish washing machine because the heat cycling will crack the adhesive.
If you expect pins to help hold the handles in place, you should use regular pin stock such as nickel-silver (for example), and the peen the pins over so that they will not pull out. Often, in the presence of sufficient force (like a dish washing machine for example), the handle material can ride right over a peened pin head, since the peened head is typically not at all large. Some people make a small counter-bore in the pin hole so that the peened material has some place to flow. Personally, I have been using a slightly tapered reamer for this purpose on the theory that more of the pin material might flow into the hole, but I have not tested this conjecture. Personally, I use a ball peen hammer for this process with a steel surface (my table saw) on the other side of the pin. It is good to check your progress now and then, because the steel surface can start peening the other side of the pin over while you are beating on the top side of the pin. When this happens, I turn the handle over and peen the other side for a while so it will match. It is not cool to peen the pin head over the plain surface of the handle material.
The best method is probably to use adhesive and bolts. There are products out there for this purpose; one is “Corby bolts” and another is “Loveless bolts” (there is at least one other kind), and these are what I use most of the time. Unlike a pin, a bolt will not allow handle pullout (where the bolt is), and when finished off they look identical to a larger pin. This way, if the adhesive bond fractures at a critical juncture, the bolts will ensure that the handle remains functional until whatever situation you are in has completed.
Mosaic pins (which I love), cannot be peened, so there is only the extra surface are of the hole for the adhesive to be to help hold the handle down. I always slather adhesive all over the outside of the pin before pressing it home, on the theory that at least some of the adhesive remains in the hole. However the hole should be a tight fit; you might want to drill small, then ream to the finish diameter.
Before applying the adhesive, I treat the under surface of the handles as well as both sides of the tang with a vigorous sanding using 220 grit paper, or even 100 grit. This process scores numerous scratches into the material, which increases the available surface area for the adhesive to adhere to. In some special cases, I have even used a moto-tool to under-cut voids into the handles to maximize adhesion. Then, I apply a volatile substance, typically Goof-Off, to rid the surfaces of any oils that would interfere with the adhesive bond. The final treatment is a thorough wash with soap and water. I then apply a liberal coating of adhesive to both handle and tang surfaces, throw in the pins or bolts, then apply clamps until I get some squeeze out. I always use blue plumber’s tape to mask the blade itself from the squeeze out. I use as many clamps as I can fit over the handles, and I protect the jaws with wax paper. Then I pre-heat my oven to ~ 120 degrees Fahrenheit, turn it off, then pop the knife handle/blade assembly and let the oven temperature coast down by itself until it reaches room temperature. The concept is that many epoxies cure best at an elevated temperature, but I have failed to do any real research on this.
After the adhesive has cured, just grind off the excess pin protrusion as well as the tang edges, which now have dried adhesive all over them. This process will also remove any tool marks that may exhibit on the edges of the tang.
I see that I have waxed a bit long here, so I hope that some of this answers your question. Also, since I don’t know you or your relative skill level, please forgive me if you already know some of this stuff; it is not my intent to talk down to you.
Oh, folding knife handles for ‘tactical’ knives (Walker Lock knives for example) are generally screwed on, but more traditional folders (Buck 110 for example) usually have the handles glued and pinned. Tradition I suppose?

Wanbasion Black Stainless Steel Knife Set, Sharp Kitchen Knife