Electrical – How to wire this 30A 250V straight blade pass and seymour receptacle

You are correct that the red should be power to the light, except the other side of the switch should take off from the line in side of the GFCI, there is no requirement for lighting to be protected by GFCI, so do not connect to the load side. The GFCI tripped because there was a mismatch in the currents between power wire and the neutral wire attached to the GFCI.

This is based on my best guess based on the information you provided. To be certain, you should examine the wiring in the other switch box to ensure the black is unswitched power, white is neutral, and the red is connected to another wire leading to the light. The main uncertainty is how the other switch plays into this scenario, as there were not enough wires for a 3 way setup with power to an outlet as well.

Incidentally, I would suggest avoiding the push-in terminals if binding screw connections are available. Doing so is more work, but it provides a better more reliable connection, provided the binding screw is properly used.

To answer your first question, no it's not permitted to have a 3 prong receptacle without the ground wire being attached. See some of the other questions explain how you should fix this situation. I believe the short answer is that it should be a 2 prong receptacle (which will be difficult to find and only to be used in grandfathered situations) or you could use a GFCI with a "no equipment ground" label.

If you use your neutral as a ground, then a neutral fault (a break in the neutral connection somewhere in the circuit) will result in the exterior of every device on the far side of that fault being an electrocution risk. You are also at risk of a shock if you ever form a better path to ground than the neutral wire.