Alya, that is incorrect. If August 20th was day 1 of a textbook, average cycle, you'd expect ovulation on September 2nd.
Not correct. Ovulation is pretty reliably 14 days before a period, regardless of its length, so you have to work backwards.
If your period is usually of 30/31 days and is usually on the 20th, 14 days earlier would be the 6th September and that would give you a clear window to get pregnant by this other man on the 7th.
Having said that, presumably sperm by your partner would have already been "in waiting" for your egg (unless he wore condoms) and would have reached it first, BUT there is some research that sperm from men that are not usual partners seems to have some advantage.
Pregnancy is usually calculated from the last period, if I'm not mistaken, so the test could actually be saying one week of actual pregnancy when you tested, which would be one week after ovulation.
Honestly, it could be either way and you should wait and test after the baby is born.
I seriously doubt anyone is going to take the blood of a child to test
It can be done with cheek swabs these days.