3. Yes, yeast go through 3 phases and in your case they have completed only 2. the third phase takes the longest as the easy work was done in the second phase and now the yeast need to break down intermediate compounds created in the second phase and clean up off flavors. This often takes more than a week, sometimes 2 weeks depending on the temperature of the beer while fermenting. Yours fermented pretty warm so it might take even more than 2 more weeks.
4. Yes, if you give the yeast something to work with such as priming sugar, carbonation drops, or DME.
5. The beer should be kept at the same temperature as when it was actively fermenting to get carbonation and maturity. This could take up to 3 weeks for the carbonation and longer for maturity depending on the darkness/alcohol level of the beer. Then it should be chilled for at least 24 hours prior to drinking with longer being better if you have the space for it.
For your next batch you should work to keep the fermenting beer cooler as you'll like the beer better in the end. Swamp coolers work pretty well for the cost. Set your fermenter in a tub of water and add ice chunks to keep the fermenting beer cool. Drape a cloth over the fermenter and let water wick up the cloth and evaporate for cooling, adding a fan to increase the cooling.
Here's some information on how the yeast cycle works by Dr. Chris White of White Labs, a major supplier of liquid yeast for brewing.