Is it possible to be ambidextrous and have a dominant hand? How would this affect tasks such as writing?

A lot of this left / right handedness stuff is a matter of habit and learning. I clean with both hands, drink with my left, write with my right and can saw wood with both and play a tune on the moothie both ways around.

People can learn to do most things if they put their minds to it. You can learn to saw wood with both hands and cut wood with an axe using both hands. Any footballer worth his salt can kick with both feet.

People often do have a dominant hand. Yes there may be a tendency to favour using one eye or one hand but anyone can learn to write with both hands if they practise hard enough. I get students who have a difficulty using both eyes with a microscope. It actually takes practice. You have to train the brain to use a microscope properly. It's not particularly difficult but it still takes a little time. Absolutely everything we do from the very simple to the very difficult takes practice to do well. Even picking up a cup takes practice. Watch a baby trying to put a cup to its mouth. It's not easy !