Hi, and welcome!
You have come to the right spot with your questions. No apologise needed of course!
1) Not all lenses are designed for the larger FF-sensor size. Sony's DT lenses for example are specially designed voor the smaller 'cropped' sensor size, as found in your A200. You could mount your 18-70 lens on an A900, but it will switch to 'cropped'-mode (reducing the effective pixel amount of the sensor).
2) I have Sony's 70-300G lens; and the Minolta 100-300mm APO lens before had that. For sports, fast focus and fast (and constant) aperture are ideal features on a zoomlens. However, a combination of both makes a heavier, larger (thus less portable) and more expensive lens. I think the 70-300G's focus speed is as fast at it gets in this zoomrange, compared to other alternatives, but it isn't exactly lightning fast. It is also quite expensive.
Sony also has a much much more affordable 75-300 lens which, I assume, is very much in the same league as the 18-70 lens.
See this excellent guide for available sony/third party options:
3) 'Is brand A really better than brand B' is a discussion of all ages. There are many professionals working with cameras which we now may consider 'old' and outdated. Next year's mid-range camera may outperform the camera which we considered pro last year. In the end, it is 'only' technology. A professional is not defined by the per-pixel sharpness of Canon or the high ISO performance of Nikon (though interesting it might be!). I think a keen eye for composition is much more important.