1) 1000 yard open water swim in less than 20 minutes
2) 200 yard run, 400 yard swim, 200 yard run in less than 10 minutes.
Start immediately! With only 3 weeks to prepare I would suggest swimming every day until your test. I am NOT saying that you should be in the pool for two hours a day busting your ass. But try to get in the pool every day from now until your test for at least 15 minutes even if it is just to cruise through a couple of laps. I do not know what kind of swimming shape you are in but I can tell you that it takes some time to get your 'feel' for the water.
Also, I would say that since you do not have a lot of time to train your 'swimming endurance' to spend some time working on your technique. Being more efficient in the water will greatly improve your chances of completely your tests in time. I am not sure how great your technique is so you will have to decide how much time to dedicate to it. If you want some good information try www.totalimmersion.net they are one of the best in the industry for technique.
As far as training I would divide up your swimming into non-stop long swims that are longer than 1000 yds (the length of your longest test) along with some interval sets.
For the interval sets I would suggest this:
Looking at the times you need beat you are basically looking at a 2 min pace per 100 yards of swimming. (That is assuming you can run the 2x200 yards in 2 min total). So I would do intervals with a 2 min base per 100. To further clarify do a set of 10x100 on 2 mins. So at 0:00 begin your first 100. 2 mins from then you should be beginning your second 100. So if it takes you 1:45 to complete a 100 then you would have :15 seconds rest before starting your next 100. For this set I would try and hold the same pace for the duration of the set. So do not go all out on number 1 and burn yourself. It is just like lifting. You can change it up however you want. If you would rather do 200s then your interval would be 4:00. If you wanted to do 50s then your interval would be 1:00.
If you can do these interval sets then you will have no problem at all completing the tests.
Also for open water swims you do not have to worry about flip turns so do not worry about them. However, I would practice swimming with your head out of water. During your test you want to swim with your head down in the water but you should lift it out occasionally while continuing to swim to see that your are headed in the right direction.
It is late and sorry if some of this stuff is not clear or if this info is already common knowledge to you. Let me know if you need more help. But right now this is a good place to start.