I'm only seeing one picture, but okay. (aahhh - reached your limit). Well, I do see a few issues right off the bat. You have some older ball and turn-type shut-off valves that are prone to going bad. In addition, you appear to have at least one indoor plumbing connection in your suction line (top corner elbow) as opposed to schedule 40 PVC that is rated for outdoor and pool use. Either of those may or may not be contributing to your air leak problem, but they are certainly worth looking at when you get a chance. Have you tried closing-off one suction line (drain first then skimmer(s) or visa versa) to see if it helps with suction? Try with red valve closed, then try with blue one closed? Give the pump a good 1-2 minutes to try and prime. Some pump manuals will even go as far as allowing up to 5 minutes or so to prime, although we typically don't like to see it take that long. If you can get the pump to prime somewhat, then you can try leak testing over those lines above ground with a garden hose, or wrap with some plastic wrap perhaps.
- - - Updated - - -
I should also mention as it's a basic item but we never confirmed ..... how is your water level in the skimmer(s). At least halfway to 3/4 up the opening? Plenty of water to suck-down into the skimmers? I know you have a drain, but we should still confirm.