If conception occurred, would a pregnancy test show positive 1-2 days after ovulation? Can ovulation occur 1-2 days before expected period?

Probably not. In a natural cycle, a pregnancy test should turn positive only about 10-12 days after ovulation, at earliest! (the exception is that in a medicated cycle, if you use an ovulation-triggering medication such as ovidrel/hcg, you can get a "false-positive" around the time of ovulation. In a healthy cycle, the "luteal phase" (time from ovulation to the next period) should be at least 10-12 days.