Neighbors(including us) around the property started to mow the part in front of their yard(the weeds grew very high) and continue to do so(is it illegal for us to mow this overgrown land?).
There are probably city codes around maintenance of lawns, cutting grass and clearing weeds. You should alert the relevant authorities and they will make sure that the maintenance occurs. You should probably not do it yourself since (a) you don't owe the owner any favors and (b) you might cause trouble for yourself.
Recently there was some mowing by large tractors but very little was cut and most of it grew back.
The question is really whether their activities bring them into compliance with applicable city codes or not. If they are compliant and you simply don't like how they maintain their property, that is tough luck. If they are not compliant, you are well within your rights to vigorously report them to relevant code enforcement authorities.
This overgrown golf course is home to many wild animals(coyotes, snakes, foxes, alligators, etc..)
See above
1) Is there any legal action that we can take to force the land owner to maintain the land?
See above
2) Could this land somehow under some law be divided and given to the maintainers.
This is an interesting question. Technically there are circumstances wherein you could take what's called adverse possession of part or all of the property. This would probably include doing things like actually residing on some piece of that land and establishing a residence there - perhaps getting mail or paying taxes there or paying utilities or operating a business - for a certain period of time without any interference from the technical owner. If you can meet the requirements of adverse possession then you might be able to become a legal owner. Unless you have little to lose, however, actually doing it might be difficult.
3) Is it legal to walk/drive on this land. (I see people walking their dogs, and driving atv's and motor bikes on the golf course)
Unless you have been given notice otherwise, it is perfectly legal to walk wherever you like. It is the owner's responsibility to provide reasonable notice and take reasonable precautions against unwanted trespass; e.g., putting up a wall or fence, closing and/or locking a door or gate, posting signs and/or hiring security to patrol the property and enforce property rights - or occasionally checking to make sure their property isn't overrun with squatters.
