A1) In desperation, I have occasionally tried fixing damages close to the stem by punching a hole through the patch and then threading the stem through the patch before glueing it down in the regular way. But as long as there is a choice I prefer to replace those tubes.
More importantly you need to figure out why you're getting damage like that. As you mention that you've run very low pressure odds are that the tire has slipped on the rim and pulled the tube with it until it tore by the valve.
This is not the oly option though, check rim for burrs while you're at it.

A2) While goop might make patching a tire more difficult it's rare that it interferes with pumping. Goop will follow the laws of gravity and physics, which tends to keep it away from the valve once installed.