Yes you need to pick up the poo
Depends on the breed and the dog
Our dog runs the garden and drags its heels on a walk and no point trying if it's raining as she isn't going anywhere
She's a small dog
I know someone with an ex race greyhound who is much the same
Plan to do 1/2 walks a day depends on how much you are at home with the dog
Younger dogs and more energetic breeds will need longer walks
Older dogs will need a walk but not as long
Children will love any dog - if you want one that will play steer from greyhounds/lurcher types as they aren't known for their playful spirit
Any Labrador or crossbreed of would be a good bet in terms of intelligence and playfulness. However you're looking at a large,energetic and strong dog. I don't know the age of your children but you wouldn't be able to allow a young teenager take them out on their own. They are strong dogs.
They will generally need 2 walks a day and enrichment
There are many breeds that are similar and different dogs have traits which makes them more or less suitable for you
Look at a local rescue and see what is on their site to gain an idea of what's out there
Most common breeds that people have/know of are typically working dogs. Labrador, golden retriever, husky, collie, even your smaller Jack Russel
All great dogs but energetic and strong (minus the jack) and in need of a lot of work so they don't get bored
Then you have your current fashionable dogs
The pugs the chihuahua labradoodle frenchies dashunds
Smaller dogs and fantastic breeds but less likely to be in a rescue
But a rescue will be over run with staffs crosses
A dog of any kind is a huge commitment which I'm sure you know