Pond advice

I’ve moved into a rental property that has a pond. I’ve kept fish before but I have no idea what I’m doing with a pond.

We have a lot of mosquitos and I’m wondering if there is any native fish that would make a good addition to the pond to keep down the number of laeve in the water without harming the frogs. I can hear a few different types of them at night so I want to restore the pond to working order. Also do I need to add a pump or filtration to it of some kind? It looks like the previous tenants or a gardener have hit the power cable with an edge trimmer, so I’ll need to replace it with something else or get it repaired. Affordable options please as the landlords are very unlikely to pay for it.

Thanks