Your lienholder will almost certainly require it.
do I have to have full coverage if the title is in my name
On every auto application, there is a question will ask: "Does the vehicle have a salvaged or branded title?" If this is the case, you will not be able to put full coverage, (comprehensive and collision coverage) on the vehicle. Sometime you can get special exceptions from your insurance carrier to get the full coverage put on if all damage was repaired. It is much harder to get full coverage on a salvaged title vehicle.
Yes you should be able to.
My insurance provider, Hanover, told me that they would only write liability coverage, and not full coverage on my truck that was flooded and totaled in New Orleans.
Absolutely you can, call your local insurance agent.
I know of no insurance company in any U.S. sate that will give you full coverage on a salvaged vehicle.
In California, anyway, you need full insurance coverage on a car the whole time it is financed. After its paid off, you can drop a bunch of the coverage and just carry liability.
In my state you only need to have Liability insurance the get a title and register the vehicle. If, however you have a loan on the car the lender will require you to have full coverage.
You cannot transfer the title while the lender has a lien on it and they will NOT release the lien until the loan is paid off. They will also NOT allow any names on the title that are not on the loan papers.
More than likely your lien holder will require you to carry collision and comprehensive coverage in addition to liability coverage, this is to protect them/their investment.
If your vehicle is being used for company/business purposes, yes.
This is your decision. If the vehicles are financed then the finance agreement you have with the bank or finance company will require that you carry physical damage coverage. If the vehicles are paid for and not financed then the decision is completely up to the owner of the business. The owner will have to weigh the risk of loss versus the premium to carry physical damage coverage.