If you allowed user to post content on social media site prior to verifying email, in order to increase conversions, how many times should he be allowed to do so? What anti-spam measures you can put in place to prevent these potential problems?
I think you are looking at it the wrong way. Limiting the number of posts isn't going to solve the spam problem.
You really have 2 problems to solve here:
Allow user interaction before confirmation
Personally, I would just force confirmation before allowing any posts, but that's just my opinion.
However, if you wan't to take your approach then it makes more sense to limit the frequency rather than the number of posts. For example: Limit new users to 1 post every five minutes.
This might even make sense for new users even after email confirmation, say for the first couple of days.
This also solves the problem of spam bots trying to flood posts, even ones that have verified their accounts.
Dealing with spam
You can't deal with spam just by limiting posting. After all, it only takes one post to post spam.
You need to have spam detection methods. It could be an algorithm that auto-detects it, or it could be a community flagging feature, or preferably a combination of both.
Then, once a new users get flagged as posting spam, you immediately lock their account until it has been reviewed. If their posts were turn out to be false spam, then you can unblock them.
In summary, force verification before allowing users to post - it's really not hard to verify an email these days.
But don't expect verification to be a reliable method of preventing spam. You need more dedicated features in place to deal with that.
In a lot of digital spaces, we let user try the platform out or use it enough times to become habit-forming. This makes sense for things like note-taking apps, calorie counters, etc.
Social sites are different -- conversion is going to come from other users' interaction with and amplification of content, not from the habit of posting multiple times.
In addition to spam, unverified users could enact many undesirable behaviors including impersonation, trolling, and harassment, which could harm your entire platform. So to answer your question, I would say no posting before email confirmation, but make confirmation as quick and non-disruptive as possible.