Now, if you are really sure that your manager is preparing to fire you, then :
"Do I simply begin looking for other positions"
Yes, right away. Keep it only to yourself.
"Do I report his increasingly erratic behavior, and waste of firm resources?"
Don't. At least not yet. It will be a waste of your time and until you are in a strong position (have already found another job etc), you will most likely weaken your position further. Remember, the company will have more interest in keeping the manager and not you. This is not the time to be a whistleblower etc and think about doing the right thing etc. The right thing to do is to look out for yourself by finding another job asap. All the other things can come later if you want.
"Do I quit before the period expires?"
Find a job if you can within the period and quit then. Do not quit on your own before finding another job.
Here is my overall take on this. You need to put yourself in a strong position before doing anything. This means that you have another job lined up. Don't worry about being blacklisted because if you do need a reference, you can always use other colleagues and not necessarily your manager. Remember the saying "most people quit their bosses not the company". And if you can find the new job before getting fired/quitting, then you anyway don't have to use current boss/company as reference because no one does that. You also will not have to explain the details of why you are really quitting.
Even though you cannot say with certainty, but whenever a manager puts someone on a "30 day review", it is most likely because they want to get rid of you. Officially, they have to do a bunch of bullshit documentation for HR and legal purposes but your hunch is almost always right.
Get out of there if you feel like you are no longer wanted. Do not confront your boss or say anything verbally or in writing. Keep it simple. Find a job, give notice to your current employer/boss in writing which should just say "I am quitting effective xyz date". Be prepared to be fired right away on the spot after your notice if they were anyway going to get rid of you. SO before sending the notice, make sure you have your desk ready to go just in case. I have seen this many times when someone is walked out of their office right away after giving notice when they were anyway going to be fired.