As to your first question, since you've had the same readings for a few days at 1.012 fermentation should be complete, and you could bottle at this point.
Question 2. Yes absolutely. Anything that will touch the wort/beer after you brew it must be sterilized. This includes your bottles and don't forget your bottle caps. Since the bottles are new you shouldn't need to scrub them with a bottle brush to clean them first. There are a few ways to sanitize them and I'm sure you can find a discussion on the forum as to which one is best/most effective/easiest etc. I used to soak all of my bottles in a sink filled with sanitizing solution like starsan or whatever else I used at the time. This way has always been effective for me, but is a little time consuming. I've recently gotten lazy and started using the dishwasher (absolutely no soap) and turning on the heated drying. I've not had any problems, but I think some brewers raise issues with this way. I've also heard of people using their oven to sterilize their bottles, but I don't know much about that and it makes me nervous.
