1. Only someone who is Gas Safe registered is allowed to disconnect the gas. It's not just a question of turning the gas valve off and removing the boiler. The gas has to be made safe, properly capped and tightness tested.
2. If you got someone in to make the gas safe, you could remove the boiler and all its water and electrical connections yourself, although you need to make sure the electrical side is safe as well.
3. The time required depends largely on what you have at the moment:
3a. For a combi, isolate the incoming cold, drain down the heating system, disconnect water pipes, disconnect prv pipe, disconnect condensate pipe (if condensing boiler), disconnect and make safe electric items, remove flue header, take boiler off wall, remove flue and (probably) make good flue hole.
3b. For a sealed heating system with system or heat only boiler, pretty much as combi, plus drain hot water cylinder primary coil.
3c. For an open vent system, isolate, clean and remove feed and expansion tank in loft, then pretty much as sealed system.
4. You might do it in 3 hours, but a slow drain down and a difficult flue removal job you could double it. This is without any time for making good.