I bought Minecraft for ps3 and two days later I had accidently broke my ps3 so Im buying another ps3 tomorrow, will I be able to still play it on my new ps3? Like redownload it from psn?
Yes, as long as you set up your new PS3 with the same PSN account. All content you buy through the PSN store is bound to your account and can be re-downloaded from your download list, which can be accessed from the main menu under "Account Management" --> "Transaction Management" --> "Download List".
You can only activate two PS3s to the same PSN account, which means you can not download and play your games if you have already used your PSN on two other PS3s. In that case, you need to deactivate at least on of these consoles.