Revert back to your lease agreement. There are terms in your agreement that cover much of this. First off, if you have a one year lease, the new owner must respect your lease...a sale of this property is not a reason for them to kick you out...your lease stays in effect even if the house is sold and the new owner must honor your lease.
The new owner, however, may try to buy out your lease for a lump some of money. That ultimately is up to you.
Secondly, all of the showings, again, revert back to your lease. In your lease there may be a provision for the owners to give you notice every time that they want to show the property. It does not mean that you need to leave. They are disrupting your work day if you work at home. There is not reason for you to have to leave when they do an appraisal. You can be home while the appraiser measures the exterior and then takes pictures of the interior.
The notice to enter the premises time is usually 24 to 48 hours. You may be a nice person and let them in with just a phone call. That is totally up to you.
Also, is your house a single family home? Are there other rental units on the property? If there are more than 2 units on this property, and if it is located in the City of Los Angeles and built prior to 1973 it may be subject to the Rent Stabilization Ordinance and many other rules and regulations apply. If it is just one unit, then it is not.
8700 Reseda Blvd., Suite 213-B
Northridge, California 91324
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Weher is the house located. You may be in a rent control area which give you certain rights. As far as leaving the house. You do not have to. As far as showings, 24 hour notice must be given to you as the tenant.
The new owner of your property inherits your current lease agreement. While they can ask you to leave, depending on the terms of your lease agreement, you may not have to.