There isn't a 'forklift license' in the US. Some companies may issue a forklift certification which potentially could expire.
yes
Yes, forklift licence must be renewed every 5 years.
yes every 3 years
Depends which country you are in.
yes it does. you have to renew it every once and a while
Most licences expire after a certain period of time in most countries and require to be renewed by the individual, they are not attached to your job/employment/employer.
You may get certified on the job, or at a trade school. If you take an online certification, you will still need to be evaluated by a qualified trainer.
You cannot learn to be a forklift operator solely online. There are safety courses and training courses that you can take online, but you have to do at least part of the training in person. You have to have an in person instructor to teach you the operation of the forklift and both practice and be evaluated by a trainer. You can find some of the safety and training course you can take online at http://www.certifyme.net/ and http://www.forkliftacademy.com/.
The training kits don't expire but the certification will in three years. Unless laws changed, that is the current status per http://www.forkliftacademy.net/
The forklift truck is driven by the forklift driver. Forklift driver must have forklift truck licence.
A Forklift operator; drives a forklift. In other words they control the forklift. For example operating the forklift to lift pallets and stack them.