Hi Janet and welcome to the Forum. Let me try this again - I just typed out a detailed message and it "disappeared". Not sure why.
First, you need to understand that mats and blades are consumables with your cutter that do need to be replaced over time depending upon how much use and abuse they sustain. One recommendation is to have multiple mats so you can not only rotate the individual mat in the cutter, you can also rotate the usage of mats. This is really useful when you are cutting a lot and need to keep loading up and inserting a mat to cut.
You are right, the pinch wheels do need to stay on the "metal spots" or "grit shafts" that are on the bottom of the cutter. They are there to keep the mat from shifting and skewing in the cutter which will happen if the pinch wheels are not gripping on the grit shafts.
There are lots of things that can cause your blade to drag. If you have too much of it exposed, if you have it set too low in the blade holder, have the blade holder setting to low in the clamp, etc. any and all can cause your blade to drag. You will want to check each item one at time and then do some test cuttings to see if you can fix it. By doing it one at a time, you will determine which issue was causing your problem. If you do them all, you won't know which was the issue. As you noted, even though you are using a brayer to try to make sure that your vinyl is well adhered, doesn't mean that it is if the mat is not sticky enough. If I am using a mat on the "tail end" of its life span, I will use blue painters tape to tape the vinyl, card stock, or other media to the mat to help make sure it is being held in place well.
There are lots of options on how to resticky a mat. Probably as many as there are people using cutters - which is a lot. Probably the easiest way is to go to the SB store and buy the "Renu Kit" or Renu sheets that Sherri sells there.
https://silverbulletcutters.com/re-nu-sheets.aspx Many people use them, I have even known people who did not have a SB who buy the Renu sheets to use on their mats with other cutters. Others start out gently washing their mats and seeing if that restores enough sticky to continue. Others, use Aliene's repositionable adhesive usually diluted 50/50 to apply on their mats. Repositionable glue sticks, etc. A quick search of the forum, or a google search should yield you plenty of ideas and information on how to do so.
Finally, as Gigi already noted, be sure to check out the Learning Center as it will have lots of information and I believe should have some of this information there. In addition, you can search the forum to find like discussions that have been had previously on different topics like this one. You can find that "search" feature in the top right side of the forum. Finally, if you need help - if you are getting frustrated and finding yourself in tears - walk away and start anew later. Often some rest and a fresh perspective can do wonders for us. I speak from experience there! Then, know that we are here to help if we can so never be afraid to come here and search for answers and if you cannot find them, ask for help. Someone will eventually come along and try to point you in the right direction!