Could I be pregnant even though I've had two normal/heavy periods since the last time I've had sex?

Not likely. Not impossible, but not likely. Really want to be extra sure? Use a home pregnancy test. Not convinced? See GYN. Most pregnancies are obvious by 12 weeks, and few have cyclical bleeding. That said it is possible to have bleeding in the first trimester of pregnancy and still have a viable embryo. If you have symptoms of pregnancy, that increases the likelihood. Not zero, but also not probable.
Yes. The only way to know for sure is to do a pregnancy test, then possibly an ultrasound. Why do you suspect you're pregnant though if periods are normal?
Take the test. If you want to know if you are pregnant, take a test. In today's world you do not need to wonder if you are pregnant or not based on symptoms. Pregnancy tests are available at any pharmacy and in minutes you will have your answer. They can detect a pregnancy 7-10 days after conception. The best time to take one is when you miss your period.