A: Since your parents were married at the time of your father’s death and they owned their home together, no probate should be required, either because they owned it together as joint tenants with the right of survivorship or as community property.
A: I'm assuming you mean an involuntary removal of a trustee. For that, you'll need to file a petition with the probate court in the county where the trustee conducts its business and prove to the court's satisfaction of the need for the removal by clear and convincing evidence of breach of fiduciary duty (stealing, negligence, failure to account, gross mismanagement of assets, failure to fairly represent the interests of all beneficiaries, self-dealing, among others). You should contact a probate attorney for specific legal advice based on your particular facts and circumstances.
A: It all depends on the court. The probate courts in San Francisco and Santa Clara County are not scheduling hearing dates for up to 3 months out from the filing of a petition for probate due to COVID.