I agree that landlord-tenant law is state-specific, so there is no federal subject matter jurisdiction. If both you and the landlord are California residents, there is no diversity jurisdiction. In unlawful detainer, the only legal issue is possession of the property, so there is no claim for money damages over $75,000, either, which is also required for federal diversity jurisdiction.
I also agree there is very little you could do to prevent the eviction. A last ditch strategy may be to find and pay a lawyer to threaten and bring a civil lawsuit against the landlord if the landlord violated any laws. You cannot counter-claim in a UD action. You have to bring a separate civil action for damages for violations such as entering without 24 hour notice, changing locks, turning off electricity, etc. You would most likely need to pay a lawyer an upfront deposit for this, as most will think, "If you can't pay the rent how can you pay me?"
No. An unlawful detainer case normally cannot be removed to federal court because there is no federal question or diversity jurisdiction.
You don't indicate whether there was a trial on the merits, or whether there was a default judgment entered.
The normal procedure if there was a default judgment is to make a motion to set aside the default and vacate the default judgment.
However, if there is already a judgment and a writ of possession issued, there is normally very little you can do this late in the game.
The information presented here is general in nature and is not intended, nor should be construed, as legal advice. This posting does not create any attorney-client relationship with the author (who is only admitted to practice law in the State of California). For specific advice about your particular situation, consult your own attorney.