Using duck pond water to fertilize orchard/garden

My husband and I dug a pond in our front yard for ducks, it's about 20x24 and 4ft deep in the center. It can hold around 13,000 gallons of water when totally full. I'm thinking that in order to keep our pond clean we will use a sump pump to irrigate our orchard/garden with the mucky water and then add fresh water back into the pond. We will also be using a solar aerator to help. We get alot of rain from fall to spring so we plan on capturing that to add back in in the summer when it's dry

I'm wondering if I'll be able to use the duck fertilizer straight from the pond, will it be diluted enough not to burn our plants. Or do I need to add it into a compost pile and let it further breakdown.

And how often should we be fertilizing our garden, is this a twice a year or once a month scenario.

I've had really good results from simply bucketing the water out of duck baths and ponds onto garden beds, berry bushes, and trees. I think that with the size of pond you've got there is no real issue with concentration. Our ducks have an old-school deep bathtub that's probably 300 litres and when it gets funky everything goes onto the plants in the general area. No problems noted.

I have read up on filtering duck pond water to keep the pond clean-ish.  Some people pump the dirty water off the bottom of the pond up onto a stone waterfall planted with plants that need a wet environment.  I do not recall any mention of the plants burning from the duck waste.  I also know some will pump the water through aquaponics tubes with plants "rooted" in the water to absorb the nutrients.
My personal experience is dumping the mucky water from our small kiddie pools towards our tomato plants just outside the enclosure and we never burned the tomato plants.
Based on this I think you will be OK.  I would do what you are suggestion without hesitation.

I would certainly use it "straight." With that level of dilution I don't think it's likely you will burn plants.

Since it's raw water, I don't think I would use it directly on garden plants that are eaten raw and could be cross-contaminated (carrots, lettuce, zucchini/summer squash -- any stuff close to the ground).

I think all of the advice you have received is really sound. I would reckon that it would be a good addition on top of a compost pile as well for a nice splash of nitrogen goodness to kick up the heat.