Pinhead
1. It varies from as little as 12 hours to several months depending on your qualifications and their needs. if you have well in excess of the minimums with international wide body time, then expect a call pretty fast.
2. Yes at least in the past they allowed you to stay longer in Dubai at your expense if you wished to sightsee a bit (a good idea btw). The hotel used to give the emirates corporate rate as well, though best to arrange it well in advance.