No you cannot include your parents in your application. You would need first to become PRs and either enter them into the parent lottery or they would need to qualify themselves for PR
Unfortunately you will have to immigrate without your parents. Once you arrive you can have them visit for an extended amount of time if they qualify for a supervisa.
It doesn't matter how you immigrate, you're parents can't immigrate at the same time. The best they can do is come as visitors temporarily.
To sponsor your parents for PR you'll need to work in Canada long enough to get 3 years of Canadian tax returns meeting the minimum LICO income amount. Then once you qualify for income, you can only enter the lottery to sponsor parents and need to actually get selected. Due to this, and the fact any future health issue could make parents ineligible, there is a possibility you will never be able to sponsor your parents to Canada. Take this into consideration when deciding if Canada immigration is right for you.
You might not need to work long enough if your world-income in the last 3years of your Canadian tax return meet the LICO income amount. Once you qualify for income, you can enter the lottery.
You might not need to work long enough if your world-income in the last 3years of your Canadian tax return meet the LICO income amount. Once you qualify for income, you can enter the lottery.