Hi and welcome!
--Do you have to keep the babies under heat lamps constantly?
Somehow they need to be kept warm enough, which is quite warm the first week (around 90 degrees F), dropping about 85 degrees a week until they are good with room (or barn) temperatures. If you are living off-grid or trying to conserve electricity, you can try a few things (try before getting ducklings to see if you can do it without making yourself a nervous wreck
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David Holderread suggests keeping their brooder box near the stove or furnace being careful not to overheat the ducklings or start a fire. In mild weather a well insulated (but still ventilated - they need air) box with cloth draped over the top and sides, with a passage for the ducklings to emerge to eat and drink, then go back in to warm up can work.
Years ago I kept Pekins and they did fine, but I got them in April in Georgia - it was easy to keep them warm enough!
--Also, can ducks & chickens peacefully co-exist in the same enclosure, or would they have to have separate living spaces?
I am told by a number of people that they can peacefully co-exist, but sometimes it doesn't work out. Depend on the birds and their people. Keep chicken water up and away from ducks, who make a real mess with water (oh, but they are lovely creatures)
--We do not have a pond but I was thinking about getting a small pool for them to swim in during the warmer weather months.
Many ducks do fine without a pond. Small pools are great, and they need to be changed out frequently (use the water for the garden)
--Do they fair well in the cooler climates?
The domestic breeds, as far as I know, all do fine in cooler climates, with some decent shelter and protection from predators and a healthy diet.
--What all does raising the babies entail? Feed, heat lamps, constant care?
Lots of duckie love!
Seriously, I don't know how someone would patiently, gently deal with the challenges of these little critters without some love of animals. But ducks are easy to love. They are sweet and funny.
I have eleven ducklings and they keep me hopping. Part of the reason is that I had no infrastructure in place until I decided to get them, and also, eleven is a big number for a suburban homestead. There are many details about raising them well, and at first it seemed overwhelming. But the main idea is - proper nutrition, clean water, warm dry bedding, safety. Branching out from there are many details. Can you get ahold of Storey's Guide to Raising Ducks? This forum has been very helpful to me with finding the wide range of ways people address each of these issues. It wasn't hard for me to find commercial feed that is appropriate. Ducklings need three times the niacin in chick feed, so do pay attention there. If you have specific questions, first search the forum - someone has probably posted about it.
--Also, can you eat their eggs?
Yes! Some people love them, just the cooked eggs, some can only enjoy them in baked goods.
--Are they like chickens in that you need a male to fertilize the eggs (if you remove them each day or however often they lay you'll be safe and not get baby ducks)?
I know so little about chickens! But I was told by a local university poultry professor you don't need a drake.
Thank you for any help. I want to be responsible about this and ask all of the important questions before purchasing. If I feel I'm not equipped to properly care for ducks, we just won't get them.
Thanks for being responsible. They are living things, and the first couple of months, need lots of care and thrive with good, affectionate attention (though my runners are skittery and I have to sit and wait for them to come sit in my lap. If I reach for them with my hands, they shriek and run away. sigh)