Personal Loan Without Established Credit

I would say no.  I answered another question on how to buy a car, but I'll repeat my answer for you.

What you need to do if you have no credit history is to buy a car using cash you already have, even if it's only a $1500 clunker off of the local lemon lot.  While you are driving this car make those car payments to yourself, using an amount you can reasonably afford (say, $200 per month).  At the end of one year, sell your car and combine it with what you have saved up (in this case, $2400 plus whatever interest).  Use that money to upgrade to a slightly better used car.  Keep repeating this cycle and after a few years you will be able to pay all cash for a new car.

This would really be an auto loan not a personal loan. I know the definition of a personal loan is a bit blurry, but for the most part, it's a loan where there is no collatoral so an auto loan wouldn't be considered a personal loan.

Yes, if you can get approved depending on your credit score. A credit union could approve you for a lower credit score though. Know your credit score first before you apply. When you apply for a personal loan, the bank doesn't care what you use the money for. I know this can be a work around when some banks won't finance a car under $5k and you don't want to go to a seedy used car lot.

simply no, why not take a few months to establish some credit.