No you can't ovulate, conceive and ovulate again, because conception turns off your normal hormones. It is possible to ovulate twice in one cycle but most experts agree that the two eggs will be released within a short period of each other (24 hours or so).
Skihorse, I would suspect in that case that one child had been carried by a surrogate or adopted. I am really not sure how it would be medically possible for one to be born and the other to remain safely in utero for 4 more months...
OWO - ovulation predictor tests simply do not work for some women. My gynae called them "worse than useless". If you have PCOS for example you may have more than one LH surge in your cycle. Alternatively even women without PCOS have times when their bodies gear up for ovulation and nothing happens, because of stress, illness, travel or because nature isn't perfect. I highly recommend you get a copy of "Taking Charge of Your Fertility" out of the library and see if that helps you get to the bottom of what's been going on.
TBH it sounds to me as though you are just having a weird cycle. There's nothing like ttc for doing that to you! I hope it works out for you soon.
You get an LH surge (measured by OPK tests) just before your af arrives. Also you get all the "pregnancy" symptoms with a rise in progesterone, just before af arrives too. So no you are definitely not ovulating a second time.
As to whether you are pregnant or not - I think that the cheap internet cheapies are dreadful at giving faint lines that are evaporation lines. Did the line on the test have colour in in within 10 minutes? or did colour come after this time? If you can honestly answer yes to these questions, then it is possible you are at the early stages of pregnancy. However the fact that the other two internet cheapy tests and the FR were negative, suggests that possibly you are just having a slightly late af. Possibly a chemical pregnancy.
The only way to know if you are pg is to wait a couple of days and test again. If that was a faint positive on the test today, then in a couple of days it should be darker.
still no AF - have used another ovulation test it was negative, the line in the PG test was there within seconds - will wait for AF to arrive now, not going to waist my money testing every day. Dont think its my month this month.
My know twins who were conceived six weeks apart! Apparently it is very rare but does happen. The mum got pregnant but ovulated a month later and got pregnant again. The girls were born on the same day but one was six weeks premature.