Responsibility for tree maintenance depends on whether the tree is a hazard: landlords are responsible for hazard trees specifically, while routine tree care on a resident's own space typically falls to the resident.
The landlord must protect the health, safety or right to peaceful enjoyment of the premises by the residents. It is recommended you invoke a mandatory mediation with them after looking through the Oregon tenants and landlords statutes and seeing if they are violating any statutes in particular.
Your landlord must provide a safe place for you. You can invoke a Mandatory Mediation with the landlord about habitability issues, safety issues, and other tenants in order to try and solve any problems you may have, especially concerning safety.
Sidewalks and other common-area infrastructure are the landlord's responsibility to maintain in habitable, safe condition, not the individual homeowner's.