Do these trannys have a filter? If not is it better to get a full flush or just a drain and fill?

drain and fill it to be safe, you wont get all the old fluid out with a drain and fill because the pan only holds 5-6 quarts but if you empty the pan every 15k you'll get all the new fluid in there eventually.
-GP-

Why isn't it safe to get a full flush?

A full flush is fine too when done right, it's just not worth it IMO. I have always believed in just changing the fluid more often and DIY.

yeah, but how many people really know how to do it right...?
-GP-

It does have a filtering media but it would be better described as a screen. Unless it is torn then it can just be wiped down with the pan removed. I just use brake cleaner to clean it along with the pan and magnets. It is a replaceable part if it is torn or damaged.