I have pcos. I took 3 HPTs 3-4 days before my missed period. All positive. And another this morning 2-3 days before my missed period. All tests were different brands and all positive. Could PCOS or ovarian cysts cause false positives?

Pregnancy tests check HcG levels which are rarely raised except in pregnancy. However, as far as cysts are concerned yes they could cause a false positive depending on the type of cyst (particularly corpus luteum cysts) but this is pretty rare.

If you don't think you are pregnant a false positive could also be caused by not following the instructions on the box for each specific test. I know peeing on a stick is a bit trivial, but there are specific "ways" and times to do it.

As always the best way to determine if there's a real pregnancy is to see your doctor and have an official test and exam performed.

It is possible, so now you need to go to the doctor for a blood test to confirm.
This early it is not as common to get positive tests on a urine test, often you have to wait till a week, often two weeks after missed period. At a few days before, were all tests with first urine of the morning ?
But in any case, I would confirm with doctor, or wait a few days and see if you get your period