Without knowing your recipe it's hard to judge your time fermenting but my schedule has always been 7 days primary, 7 days secondary with dry hop, otherwise 2 weeks in primary, you do not want the beer sitting on all the trub for extra long periods of time. Always check your gravity a couple days ion a row to verify your fermentation is complete.
2/3 cup priming sugar is the general rule for a lot of beers and no, you do not just dump the sugar in the beer (after fermentation it is no longer wort). YOu dissolve the sugar in 1 cup boiling water, cool and add to bottling bucket, then siphon into the bucket and it self mixes, then bottle away! I can usually get good carbonation in 1-2 weeks depending on the temperature. I like to bottle condition for 3-4 weeks to let the flavors mature a bit but have been know to sample a few in the process. Bigger beers will like more time-Cheers!