I just installed a pressure tank to replace one that seemed to cause cycling.

A little background:

1. Bought a home and a few weeks ago, home inspection found no issues with water system. In fact, inspector made a point to say how great the water pressure was.
2. Right after moving in, I noticed the water pressure would lessen every two seconds. After some advice, I pressed in on the air stem valve on the pressure tank and water squirted out.
3. I drained the tank then realized I needed more tools before replacing the tank. So I then put things back together and refilled the tank as I needed water for the evening. Funny thing was that the cycling was no longer every two seconds. It was now a two minutes or so, which still isnt good. So im not exactly sure how it got better by just draining and refilling.

So now I have replaced the tank. It looks like I will have to re-do some of the work as I have a tiny leak on a poor solder job I did on the copper, a tiny drip from the T connection to the tank, and condensation on the flex pipe that goes to the main connection at the wall that leads to the pump/well.

Besides fixing some of the drips, there still seems to be other issues. The cycling isnt frequent but it will still cycle less than 5 minutes of running water. I also hear what sounds like air around the pressure tank when cracking the drain valve on the T. The pressure tank is 34 gallons.

Did I just do something completely wrong? Should there be air leaking when I crack the drain valve? This is a new tank, 30 something gallons....shouldnt it keep the pump from cycling every few minutes when just running the sink, for example?

I have also looked into the CSV valves and I do plan on getting one but I need to look more into where it needs to be installed. If its in the well, then itll have to wait longer because I just dont have the kind of time right now. I also need to get this resolved as quick is possible. I have so much on my plate and still need to unpack from my move lol.

I guess I shouldve just called a professional. I was trying to save myself some money as the quotes I got were expensive.