Is it feasible to build a fish/duck pond in my back garden?

Assuming you are allowed to do so, yes it can be done.

But can you afford the time and upkeep?

You would have to excavate the planned area.

Install the pond liner and decorations.

Install a circulating pump/filter/aerator if necessary (requires electricity).

Get the appropriate chemicals to treat the water without harming aquatic life or birds. (regular costs and time too).

And of course heat the thing in cold climates (more costs).

Takes work and MONEY to build and maintain it, plus the time.

Oh and you need to buy plants and fish to stock it.

Fish may need fish food too.

Every so often you have to clean out the bottom as organic matter will build up - more time and money.

You may have to pay more insurance too. Or install a fence around it or your property.

Check with your home insurance company before doing anything.

Then check local ordinances and such.

Yes, but they are for only certain people.  You will have to determine if you are one of them.  It will cost more than you think, will be way too small for what you want, be a lot harder to maintain, And, most important, you will have to be willing to get filthy on occasion.  Fish poop and pee a lot.  Also, you probably won't build it right the first time.   That is why you have to really want one to do it.

Anon has it spot on. We did it. Look online.

Bylaws, you need to first check local bylaws to make sure it is permitted. Then you need to check dig safe or whatever it's called. To ensure that you can safely dig. You also must know the frost lines and such so you can dig deep enough so the entire thing, doesn't freeze and kill your fish.

That's all research crap, digging, designing, and such. Is really not all that difficult and everything you need to know. Can be found on line.  If you have the back, go for it, keep in mind, the more direct sun, the more water plants you'll need.

Depends on your local zoning laws and ability to get a permit.  Also depends on what your soil is.  If you are on granite, you might need to blast.  If you're on sand, you might have problems keeping the pond full.  

Yes. Dig a big hole, put in a pond liner, fill it up with water; add paving around the edge and a few marginal plants: job done. Loads online about it.