1) No but he may. The Problem Tenant's (PT) actions are probably breaching a term of the lease. If so it is grounds for eviction.
2) Possibly. Depends on the lease.
3) You can file a police report for trespass and littering. You could also file a suit against the PT for any damages you sustain, like punctured tires.
4) Depends on the type of lease and length of time the PT has lived there. If it has been over a year 60 days is standard.
Good luck, I hope this has been helpful.
-Michael R. Juarez Law Office of Juarez and Schaeffer PO Box 16216 San Diego, CA 92105 (619) 804-4327 www.jslaw.org Mike@jslaw.org This posting is provided for “information purposes” only and should not be relied upon as "legal advice." Nothing transmitted from this posting constitutes the establishment of an attorney-client relationship. Applicability of the legal principles discussed here may differ substantially in individual situations or in different jurisdictions.
As an initial step, you may wish to consider trying a local landlord tenant or neighborhood mediation program to defuse the dispute with the neighbor. Below is a link with a list of community mediation programs.
To answer your questions:
1. The landlord is not obligated to evict the tenant;
2. Depending on the lease, this may be grounds for the landlord to evict the tenant, but you would have not right or standing to try and evict the tenant;
3. You could file a police report, but they may not do anything about it. You could file a lawsuit against the tenant or seek a restraining order;
4. What type of notice that would be required depends on the lease and the type of tenancy.