1. Do people even give a hoot about Class systems anymore or are you discouraged by them?
I think different classes opens up the replay value. For example mixing different classes, or going it alone with each separately.
2. If a game did have one would you prefer to be able to change classes at will or a "One choice and you’re stuck with it" system?
Be stuck with it, unless it is similar to your current one. A soldier shouldn't suddenly be infused with magical abilities but he could learn archery, experiment with herbs and then become an apothacary. A Cleric might dabble in the dark arts or learn the bow.
3. Exactly how should the Class system impact the game in your view, for example, like FFV where the story seems to revolve around it or more like an extra add-on?
If you could make the story differ depending on your class (prejudices, different methods) that would be most exciting, otherwise it would simply change the difficulty. (Like an elf might be better at riding the magical unicycle of Thermos, than a dwarf)
4. Do you prefer classes to be restricted to what kinds of equipment they can use or do you prefer more freedom in that department?
Again, a pansey Elf shouldn't be able to wield a battle axe and dwarves should stay away from the leotard.
5. Should Class skills be learnt as you level up or acquired though other means? (Such as buying them with Points or the like)
Most skills should be learned as you progress, with special extras available from training or side quests. We all learn to walk, but not everyone learns to drive. It can make life easier or (in my case) become a useless skill.