My advice, as someone that vacuums pools for a living, would be to connect the hose directly into the hole at the bottom of the skimmer. Using a vac plate will only create a bunch of problems with getting a good seal, and you will have to disconnect it every time the basket fills up.
I'm assuming this is the first time you are vacuuming this pool since it was opened, so there is a significant amount of debris in it. Yes it is possible to clog the pipes underground if you vacuum up too much too fast, especially if you suck up twigs. They won't travel around a bend or an elbow in the pipe, and other debris will get caught on them. Your best bet would be to get a leaf trap. A leaf trap is a canister that attaches to your vac hose that catches the leaves before they get to your skimmer. It will prevent clogs, and is easier to empty than the pump basket, which you would have to deal with if you didn't use a leaf trap.
You said that you don't think you are getting enough suction. This could be caused by any number of things. I would start by checking to make sure that you have isolated the skimmer you are using by closing the valves to other skimmers or drains. You want all of the suction created by your pump to be pulling through the skimmer you are using to vac the pool. The valves you will need to close will be on the front side of the pump. If there are valves on the pipes after they come out of the top of the pump, they are return lines, and should be left open. If there aren't valves for other suction lines and skimmers, you should plug them while vacuuming to get the same effect.
If you have checked the valves, and you have isolated the skimmer you are using, but you still aren't getting suction, I would check the pump basket. If it is full, it will restrict the flow through the pump, and if left that way long enough, will burn out your pump. This basket should be emptied after every time you vac the pool.
It sounds like you aren't sure if you are losing prime or not. If you lose prime, the water coming out of your return jets will stop, or at the very least, drastically lose pressure. You can also tell by looking at your pump. If you can't see water moving through the pump, it probably means you have lost prime. Sometimes you will be able to see a trickle of water coming into the pump. This means you lost prime, but the pump is starting to pick it back up. Give it a minute, and you will see the trickle get bigger and bigger until the pump is full again, and suction comes back to the skimmer and you will again see pressure at the returns. I wouldn't rely on a pressure gauge alone to know if things are running right. They fail way too often to be reliable.
If you have isolated the skimmer, the pump basket is empty, and you have good prime, I would recommend checking the pump impeller. If you remove the pump basket, you can reach down into the hole in the back of the housing. This is where the impeller pulls in the water. If debris somehow got past the basket, it often clogs up in here. Pull out as much as you can. WARNING: make sure you have shut off power to the pump completely. You don't want the timer to kick on while you have your fingers in the impeller.
If you have tried all of this and still aren't getting good suction, chances are it is something that will require more extensive disassembly. It could be a filter issue, or a broken or collapsed pipe underground.
I've given you a lot of information to process here, so feel free to ask questions if you need clarification on anything. Hope this helps. Good luck.
