Liability insurace (in case you damage something or hurt someone) and, if you have enough employees, Worker's Compensation insurance to cover your workers that get hurt on the job.
my way
It may not be a requirement of the company you are cleaning for to have liabillity insurance but it will help you get more jobs if you do.
house insurance
Yes
You need a commercial general liability policy.
If your dentist tells you you absolutely need a teeth cleaning and writes the insurance company they will cover their portion of the cleaning.
GL or General Liability
The contractor should be bonded and carry liability insurance and you need to require proof of this before they start. Homeowners insurance is not meant to guarantee work on homes.
Most insurance companies would be able to provide this kind of insurance on multiple properties in multiple locations. Insurance companies do not need to be local to the property that they are insuring.
You do not need a cleaning license for Texas but you should always carry liability insurance and have a surety bond. This will protect you against any claims that may occur associated with you work.
While insurance is not required to complete office cleaning jobs, it is certainly a very important need. Most companies want to hire someone who is bonded and insured; this protects them from damage and theft. In addition, you will want to protect yourself from any potential lawsuits.
You will need to contact an agent(s) for a quote.