Florida Above Ground

So I recently moved into a rental home with an above ground pool, approx. 15,000 gallon, its a 15 x 30ish oval. Has one drain which is a top skimmer and one jet. Has Hayward pump and Hayward de filter. So I have a few questions.

1- I added de to it right after we moved in and after about a month it started to turn a little green, so I pulled the filter apart and it was covered in green de powder so I would just thoroughly and put the filter back together and get the air out etc. and add more de. My questions about this are can I bump it when its like this or do I need to clean it the way I was? how often should I bump it?

2- Only having one drain and one jet both being basically right next to each other and toward the top of the pool I don't seem to get very much water circulation towards the other end of the pool and basically no circulation at the bottom of the pool so it seems like all the leaves, algae etc just settle to the bottom and its hard to keep it clean. Any ideas to get better circulation to the bottom and other end?

3- I also do not have an auto chlorination system, so I have just been added tablets to the strainer, will that be an ok method? I also shock and add liquid chlorine if necessary, which seems to be more often than not.

4- How long each day should the pump run? Being in florida and getting the algae and stuff in the pool right now I am running it like 8am-noon and 530-1030 approx. times, it is on a timer. Is that enough, or too much, or not during the right times.

I believe that is it at the moment. I appreciate the help, it seems that I can keep it clean but it is always for no longer than a week or so and it gets dirty again. Any tips are greatly appreciated.

1 - I can't help much, I only have experience with sand filter (and Intex carts). I can tell you that DE will clog very fast if the pool has live(green) algae.

2 - Best you can do is point the eyeball down and away from the skimmer.

3 - Several things: Tabs in the skimmer when you use a timer can be a problem. When the pump is off, the tabs dissolve into a small amount of still water. Tabs make the water acidic and when the pump starts it gets a "hot shot" of very acidic water. Tabs add CYA to the water, uncontrolled CYA can lead to a green, unsanitary pool as higher levels of CYA requires higher levels of Free Chlorine. How do you shock (thanks of using it as a verb) and under what conditions?

4 - If there's green in the pool, run it 24/7.

My advice: I think you need to get control of this pool sooner rather than later. You've come to the right place.
1) Get a Taylor K-2006 or K-2006C test kit (accept no substitutes). You can't buy it locally, you'll have to order it online. Log out and check the links in Watermom's and PoolDoc's signatures for where to buy.
2) Please navigate to poolsolutions.com and read the guides there especially the Best Guess chart. I believe it will explain what you are experiencing.
3) Log out and read the stickies on the chemistry and algae forums here.
4) Tell us how much of what (chemical names, not brand names) that been put in the pool this season and when it was added then someone here may be able to help.
5) Did you order that K-2006 yet?