You should be able to post in this section; you just can't post in the Getting Started any more.

1. GFCI units aren't fixable. You wouldn't want to fix them in any case -- you couldn't be sure it was safe. Is the GFCI unit on the cord, and external to the pump?

2. You can maintain the pool with bleach and dichlor, but keep the chlorine high and DO NOT SWIM! If you load the pool up with swimmers, when you have no filtration, you're likely to end up with a swamp.

3. If the GFCI is external, you can cut it off, and rewire a new plug onto the cord. You'll need a separate GFCI; your pool won't be safe without one.

This plug replaces the male plug on your extension cord; you have to cut the cord and rewire it. You *may* be able to use it to replace the GFCI on the pump
Leviton 16693 15A 120VCompact Right Angle GFCI

This is a simple plug:
Leviton 660-515CV-0CV 15A 125V Male Connector, Yellow

I'd recommend that you get those models from Amazon; similar products are usually available from Lowes or Home Depot, but they have unsuitable products mixed in with suitable one, and you have to read labels very, very carefully . . . and know exactly what you're looking for. If you need appropriate extension cords, here are 2:
US Wire 74050 12/3 50-Foot SJTW Yellow Heavy Duty Lighted Plug Extension Cord
US Wire 74100 12/3 100-Feet SJTW Yellow Heavy-Duty Lighted Extension Cord

Ideally, you'll put the GFCI on one of these, and the plain plug on the pump. That way, the GFCI will be off the ground and semi-protected.

Finally . . . I'm guessing your GFCI lay in a puddle? Don't do that! The new GFCI won't have that problem -- IF you put it on the extenstion -- since it will plug directly into your receptacle. But make sure the extension cord / pump plug connections are raised off the ground, too.

Here's another option:
TRC 26020008-6 12/3 GFCI Protected Tri-Cord Set 3-Outlets, 2-Ft, 15A Yellow