Your first plan of action IMO is to fish the ponds with simple methods such as small bobber, a number(#) 6 aberdeen hook and pieces of worms or crickets for bait. You should try and find out what types of fish live in each pond. Keep records of what is caught in each pond. You can take pictures of what fish you do NOT recognize or know their common names and we can help with identifications. There are some simple fish sampling methods that also should be used to get an idea of what fish species are not sampled well by angling.
You can probably ask your neighbors about their ponds. Most people that actually manage their ponds are happy to talk about it.
Second plan - You an be talk to some of your new neighbors with ponds. Yes - most people that actually own a pond are happy to talk about it.
When talking to locals about pond management be cautious what they tell you. Every pond owner thinks they are an expert. Most times they are not experts but want to be an expert. They know just enough to get you into some sort of difficulty. Every pond even each of those on your property are unique and different, just as all people are different. Ponds are complex ecosystems.
Take what local pond owners say and come back here for second opinions and more advice that is probably more experienced - some of it definitely will be professional and with lots of experience. For instance I have a MS in aquatic biology and have been doing this type of stuff for over 40 years.
Cow manure in it self will not leach toxic substances into the pond any more that bird or critter manure that is deposited into the pond. Cow manure probably does not have more harmful toxins compared to the harmful air pollution chemicals that get deposited into the pond during rain events. Rain strips lots of air borne chemicals out of the air such as acid rain. However the manure has basic nutrients in it that make the pond grow all sorts of more stuff including fish and plants. Manures are common types of fertilizers used for organic crops.
Some fish farming can be done in your existing ponds. However you need to formulate some realistic goals of what is already in the ponds and the depths of each pond. Then decide on what are your goals for farming some fish. Know maximum depth and average depth of each pond. Then you should get some water chemistry tests of the water for concentrations of the basic pond management chemicals. If each pond has fish in it this is a good early sign the water quality is at least good enough to grow fish year round. Often different species of fish are tolerant of different types of water qualities.
Usually fish growing ponds are specially built depending on the goals for the types or species of fish that are going to be raised. You don't just dig a hole.
