Summary: (a) no; (b) not to any significant extent; (c) no, due to (b). You'd get about 80 miles / 130 km from cruise altitude.
Any aircraft can glide, whether or not it is designed to be powered. The two main factors that determine glide distance over ground are glide ratio, and sink rate.
Glide ratio is the horizontal distance travel per unit height. A modern club-level glider has a glide ratio of about 40 to 1: it will glide 40 feet forward for every foot of altitude. High performance gliders approach 60:1, old basic trainers closer to 20:1. The glide ratio can also be expressed as the ratio of lift over drag, or L/D. There is one speed at which L/D is optimised, and this is the speed at which you will cover the greatest distance for a given altitude. In gliding we call this speed "Best L/D" and in still air it is the most efficient speed to fly when you want to cover ground (such as between lift sources).
You see many unsubstantiated figures for airliner L/D ratios, anywhere from 10 to the high 20s. Given that to test this you would have to stop the engines entirely, needless to say it is very seldom tested! The famous Gimli Glider (a 767) achieved about 12:1 which sounds pretty good for dragging those huge engines through the air. That glide was flown at 220 knots based on the judgement of the captain, an experienced glider pilot.
The interesting thing about L/D is that it depends solely on the aerodynamics of the aircraft, and the airspeed. Weight does not affect L/D, so claims that "gliders are light" are misleading. Increasing weight increases the best L/D speed, and (solely as a consequence of the higher speed) the sink rate, but has no effect on the glide ratio. In fact in the right conditions, competition gliders are often ballasted with hundreds of pounds of water to increase their best L/D speed, and so get you round a course faster.
So in still air, from say 36,000 feet that 767 could glide about 12 times its altitude: 70 nautical (80 statute) miles.
But what about lift? Gliders gain altitude by flying in rising air: thermal, ridge, or wave lift. Lift can vary from 100 ft/min (a weak thermal) up to 1,000 ft/min (strong wave lift). So a 40:1 glider flying at its best L/D of about 60 knots, is going down through the air at 60/40 = 1.5 knots or about 150 ft/min. Any time you are flying through air that is rising faster than 150 ft/min, you will climb. That's how long duration gliding flights are achieved.
The catch with the airliner is that it is gliding at 220 knots at 12:1, so it is sinking at 18 knots, or 1,800 feet per minute. Except in unusual conditions the aircraft is unlikely to fly through much more than a few hundred fpm of lift on average, at very best. So lift can be largely discounted and the distance covered over the ground stays around 80 statute miles from cruise altitude.