'AAA' isn't a very well defined term, usually meaning "over $10M budget" in my experience, or just the comparable quality to the other big-budget games ;-)
The proposal made is for an AAA Open World game for console platforms: PS4 and Xbox One to be specific.
Having a brand new studio that's never worked together before, trying to produce a project like that, is a pretty big risk.
A small console game team would be about a dozen programmers and a dozen artists -- though this isn't quite up to the "AAA" standard... More the budget developer who might produce a rough game that still might rate well or become a cult hit...
- What is the average number of personnel a small Development Studio [From software engineers, to programmers, animators, testers and so forth] needs to develop an AAA cross platform game in a time span of Two years? What are the least number of people and their specialties needed?
For bigger games, just check out the credits sections on games that you're comparing your own project to.
If you have some senior/experienced console engine programmers on the team, and you're prepared to stay in pre-production for a year before ramping up into full production mode, then maybe ;-)
-Would the option of building your own game engine [weighing in the time factor in doing so] be better than using existing game engines out there?
Otherwise, CryEngine/Unreal are very affordable these days, plus many workers already have experience with them...
Yes, assuming you've also got a highly experienced team of console game programmers to make proper use of it!
-Are there top notch Game Engines out there that can create an Open World, sophisticated, modern videogame for PS4 and Xbox One?
I've worked on a bunch of $3-5M console games, some involving big IPs but I wouldn't call them 'AAA'...
-I am aware that the cost can go up to 10’s of millions, so I risk in being candid that my projected proposal is between 3 to 5 million US dollars. Have you heard of Studios that have done so with such a limited budget?
If you've got the budget up front, that's obviously a constraint on the planning. You may have to compromise a lot on the game/world in order to stay in budget.
Also, developing the game is only half the cost -- marketing/selling it can cost just as much as making it! Does your budget cover publishing costs, or do you plan on partnering with a publisher?
Its going to be extremely game-specific... You'll optimistically want a fairly complete design, and then a collaboration between the designer, a lead programmer/technical director, a lead artist and a decent producer / project manager.
-Is there an existing business plan out there I could use as an outline?