Morning Odai,
Time frame to get started can be very short. You simply pay the course fees (or part thereof, see below) and can get cracking straight away. If the brush-up timetable of the school in question doesn't fit with what you require, you might want to consider looking at another school. My provider (CATS) offer quite a bit of flexibility in this regard, with each of the three stages having three or four brush-ups per year. You can also chop and change subjects, and complete the exams in more than three sittings, if this suits.
In relation to the specific questions:
1. You are right to be concerned about your provider going bust mid-way through your course. To guard against this consider negotiating to pay, say, half the fees up-front and half on commencement of the final stage. This is what I have done. It doesn't eliminate risk totally but gives you some downside protection.
2. The main update recently has been the change from JAA to EASA, but not all the subjects are featuring EASA questions as yet (as far as I'm aware). Ultimately the underlying subject matter doesn't change that much, and question banks are a useful method of spotting new questions. I'm actually using JAA BGS materials for my course, and then cross checking the syllabus against CATS materials for updates in the run up to each set of exams.
3. Obvious not a voice of experience, but I can't really see why an airline should care about how many sittings you have taken, or the length of your course, so long as you have achieved first time passes and high scores in each subject. After all by definition to do this you must complete the course within the 18 month timeframe from first to last exam set by the CAA.