if you have access to a baby pool or similar, i would definately pump the water from the pond into it and put the fish there as a temp home. i would have a pump ready to go when i did this then you could clear out all the seaweed, and other plants long enough to clean up the pond. run the new pump in the baby pool for aeration while your working. i dont know how long this clean up will take so if you can get it done real quick it would be best. but you can select the plants you want and thin them out. it looks like you have a ton of hornwort.(although you could have supplied better pictures). get your filter set up and ready. put the plants you want back in the pond, but rinse them off before returning them checking for snails, leeches etc.. fill and dechlorinate the pond...if it were me i would leave the rest of the plants in the baby pool and set things up as such: pump in the pond feeding the filter , the filter feeding the baby pool, this way the baby pool is basically a veggy filter or bog...then the baby pool spills back into the pond. this would aid in getting a smooth transition for your fish and pond...i would also get some bacteria to seed the pond and filter, it will make the whole process much quicker. when things are stable remove the baby pool from the equation.
