Yes you can race on the freestyle, prob for as long as you want to. The biggest difference is race bikes are purpose built for speed and go way faster. If you're just doing it for a bit of fun there's no probs, but if you want to be competitive you'll need a race bike.
20 or 24in..... now you're opening up a can of worms
Really, it's up to personal preference. 20 are faster and 24 more stable(that why they're call cruisers). Prob like the difference between an F1 car and a Bathurst supercar. I came from MTB and only went to BMX when my kids started racing. I got a cruiser first, and it was fast and scary but I always felt like I just couldn't get enough drive etc. Then I built up a 20...... massive difference.... and F A S T!!!! Absolutely love the 20. But that's just me.... haha
Just race on your freestyle bike and test out some of the 20s & 24s at your local. You'll work out pretty quick what you like.