The officer barely speaks English and there is no interpreter. What should I do?

Baseline tactic: cooperate to the minimum, sign nothing.

• State your name and show your document. This can be done without a common language.
• After that — stop. To any questions, demands to sign, or requests to explain something — a short "I do not understand. I need an interpreter." Repeat as many times as necessary.
• Do not sign any document until an interpreter has translated the content. Your right not to sign what you don't understand is well established — you may add a comment in your own hand: "The text has not been translated to me, the content is unclear."
• Insist on an in-person interpreter, not an online/phone one. If a phone interpreter is offered, politely decline: "I need an interpreter on site."
• Call your own lawyer. In your own language it is the lawyer who will actually explain what is going on, and it is the lawyer who will tell the police that you refuse to give any statements without an interpreter and defence counsel.

What not to do: don't try to "work it out with gestures", don't sign anything "just in case", don't accept a random bystander as an interpreter. That is a standard way to get you to endorse things you would never sign.