Yes, you can post it to multiple subreddits. I do it. What happens depends on the mod of each sub. Some don't care, others will see that you posted it in multiple places and take action (delete your post, ban you from the sub, just warn you, etc.)
They can detect all sorts of spamming there. Pretty difficult to do with new accounts, you need to build several up under different IPS over weeks or months and get karma
Scan the subs you want to submit to. Sort posts and find ones from like a week ago. Click on the username and look at their post history. If you see duplicates all over the place, you're safe. You'd be surprised how much info you can learn about Reddit by browsing a blatant marketer's account. Whats really fun is discovering an under cover marketer. Or, accidental marketer. Sometimes you can't tell the difference...