How to store Latex paint for the long term – a decade or longer

I wouldn't try to scrape off the messed up area while it's wet because you'll leave ridges at the edges of the area, which will look even worse. Leave the area to dry before trying to fix it.

To get it to dry quickly, higher temperatures and low humidity are your friends. I've used a space heater and an oscillating fan when I needed paint dried quickly: arrange the heater and the fan so that warm air gets blown past the work piece continually. Leave it running overnight: it looks like you're using a higher-gloss paint, which will form a skin quickly, but underneath will remain wet for a while.

(See here for a technique for removing drip marks.)

Latex paint can generally be thinned with plain water... but I'd test with a very small quantity and a piece of scrap wood first. If you can't get a good consistency, there are thinners made specifically for latex - SCL-Sterling makes one called Thin-X Latex that I used a while back, with good results.