The recommended routine is 3 sets of 8-12 repetitions, with no more than 30 seconds between them.
Then rotate around your exercises until you've done them all. Keep similar ones apart so that the tiredness of one muscle doesn't prevent you from working another one hard.
Correct. Especially if your goal is gaining muscle. You should only work out 3 times a week, and keep changing order of the exercises, days and time during which you exercise. "Surprising" your body that way, is the best method for avoiding gain platoes. If you keep your routine short and focused (minimal breaks between sets - overall no longer than an hour, hour and a half), you may even be able to skip cardio altogether.
I also highly recommend natural supplements - like Creatine (go for tablets if you can afford them, better absorption than powder), and Whey Protein.