4. Is there any particular difference between machines you learn to fly on? I mean, is Cessna very different from others?
It depends on who you ask. Ask a Cessna Sales Representative and you get a completely different answer than what a mechanic, instructor or pilot would give you.
Having said that, from a pilot perspective the flying characteristics between the two most common training aircraft (PA28 Piper Warrior and Cessna 172) are pretty much the same. Cockpit layout, the way the systems are setup and controlled, are all pretty much the same too. Once you have your license, all that's typically required is a browse through the POH (Pilots Operating Handbook) and an hour checkout flight and you're good to go. Legally speaking you don't even need the one-hour checkout, but you do need to be familiar with certain bits of information contained in the POH.
The same applies for performance. The far majority of the rental fleet is based on a 160 HP engine, burns about 8.8 USG of avgas per hour, and cruises around 100 knots. They can carry four adults with half fuel (about 2.5 hours endurance) or three adults with full fuel (about 4.5 hours endurance).
So the only real difference between a Cessna and a Piper (or Robin, or Bulldog, or whatever) is the view. A Cessna is great for sightseeing as the wings are not in the way of looking downward. But your head is essentially in the wing, so the view sideways and up is severely restricted. Low wings are better for looking sideways and up, but if you look down the wing is in the way.
So to a very large extent the choice of aircraft comes down to preference and availability. It's a good idea to stick to one aircraft type during training, but once you have your PPL it's very common to get checked out on a number of other types, so you have a choice based on availability, preference and mission.