Please find my answers below:
1. You just need to add the code mentioned in this to get images on posts. You don't need to buy any addon: https://wpforo.com/community/how-to-and-troubleshooting-2/uploading-and-embedding-images/#post-5212
2. You can use this code to enable Youtube embed without any addon: https://wpforo.com/community/general-discussions/original-wp-embed-function-for-youtube/#post-1875
3. The Private Messaging is a profile builder plugin specific function, this is not forum specific feature. wpForo already allow your users to set Topics as Private and discuss privately. There is no any forum plugin for WordPress that comes with built-in private messaging system. But there should be such plugin for profile building and membership.
@trong You can install buddypress for private messaging and notification system till you manage to buy an addon.
