1. Pertaining to the cartoon:

1. Was it ever stated as to what happened to the Autobots/Decepticons some 300 years after the great war?

2. How long did the Beast Wars last? I'm pretty sure it was a few years at the most...

 

Autobots won the Great War and assumed control of Cybertron. Put the Decepticons down in a serious way.

Decepticons mostly retired, but some were rebuilt and reprogrammed as Predacons (ala' Ravage). All, or nearly all, Predacons/Decepticons are forced to live off-world. It's pretty much their punishment for starting a millions-of-years-long war. It's also very likely why you never hear about the Predacons in Beast Machines, since Megatron was only wiping out the population on Cybertron itself.

It's generally assumed that the Autobots and Decepticons are nearly extinct once the population is upgraded to the more fuel efficient Predacon/Maximal bodies. However, in Beast Machines there are scrapyards filled with giant Autobot bodies, all recently taken offline. Take that however you want. The population of Cybertron very well could've been a heavy mix of both Autobot and Maximal. It's really up to each individual to decide how you want it to be.

And you'd be correct. I don't know an exact number of years, but generally I just assume it was about 3 years- the running time of the actual show. I guess you could take Chak and Una as evidence, since their tribe shows up in season 2 and they're never shown aging beyond a year or two by the time the show ends. There is one episode where it's shown snowing on the Axalon, so the seasons did make one full rotation for sure. Other than that, your guess is as good as mine.