I've never brewed a Kolsch, but I think the recommended fermentation range is around 60, followed by a lagering step at around 35. I think you'll end up with way more esters than the style would have, but that doesn't mean it won't be drinkable. It may still be good, just not like a Kolsch.
So, to answer your specific questions:
1. I'd say it's too late to fix the temp issues. You should have pitched the yeast at around 55 deg to let it rise up to 60, and kept the fermenting beer in a cool box or converted fridge/freezer. You may be able to keep the fermentation temps down with the wet tshirt trick, but I don't know if you could get it down that low from your stated temperature range. But, you wouldn't be able to lager it properly anyway.
2. Let it go. It may be a good beer. But it will probably be more ale-like.
3. The negative effects are more esters, and possibly fusels. If the beer's temp (which is more important than the room temp) gets up into the 80s, you may get solventy flavors in the end product from the fusels (and possibly bad headaches from drinking it). Not necessarily, but it could. Esters, on the other hand, are what give ales their fruitier aspects, and they are intended. Again, the beer COULD be delicious as a result, but it won't taste like a Kolsch.
4. If on a budget you mean you don't have a cool box or dedicated fridge/freezer with a temp controller, you should stick with ales. Lagers or low-temp hybrids won't do right for you. Most people start with ales and brew them for quite a while before getting lagering equipment. That's what I did.
