I doubt there is a municipality anywhere that would allow you to boot a tenant if they have a valid lease agreement in place. Even after you close on the property, you will probably need to wait for the lease to run its course (or take the proper steps according to local month to month lease stipulations if no rental agreement exists) unless you can reach an outside agreement with the tenant (not the current owner). Most state landlord-tenant acts are very tenant friendly.
Kudos on your plan! My first purchase was a 6 unit building in 1994, that was the best purchase we ever did and it gave us a great multiplier effect when rents went up. We refinanced a year later to pull out the downpayment for our first single family home. You can negotiate with the seller to have them vacate a unit. This depends on how strong the market is and how cooperative the seller is. If you are in San Francisco or another rent control city, please check on the local rent control ordinances. Issues involving "protected" tenants may hamper you moving in to the unit of your choice. Best of luck!
In order to terminate a tenancy, you must be the owner of the property. Thus, the short answer is no, you would have to wait until you become the owner. However, you may have the seller serve the termination of tenancy notice prior to close of escrow anticipating your need to have the unit vacant.
You also want to make sure that you read the current lease that is in place. If they are in a month to month or at will term, you can give notice and have them vacate...you may have to pay to move them. If they are in a long term lease you will have greater difficulty.
Depends on where you are and what the city/county rental rules are.. If you live in Los Angeles or Santa Monica you might have to pay a relocation fee to the tenant. If you live in a city in the South Bay where there is no rent control then there is no problem as long as you give the tenants proper notice