A neowalker is a planeswalker post-mending.

An oldswalker is a planeswalker pre-mending. Much more powerful.

The most important distinction between Oldwalkers and modern 'walkers is their physical form (and this speaks to nearly every point you bring up). Oldwalkers transcended physical form; their body, clothing, appearance, everything was constructed by sheer force of will. They were immortal in the Greco-Roman pantheon sense of the word; they did not age, they did not die of natural causes. Suicide was an option, by simply willing themselves not to live. Incredibly powerful attacks could kill them, such as in duels, or when Urza activated the Titan Engines on Phyrexia, but everyday battle scars were easily shrugged off. (Yawgmoth believed that the spark was located in the brain; he tortured the planewalker Dyfed by embedding a powerstone dagger in her brain and scrambling it around. This prevented her from being able to escape or change form, and allowed his followers to vivisect her.) They were, effectively, gods. They had access to near limitless supplies of mana, and could shape worlds to their will.

Modern 'walkers, after the Mending, are normal mortals. They can be hurt, they can die, they can't change shape (at least because of their spark; with enough study they could learn such tricks). They age like normal members of their respective races, they have to study and learn to become skilled mages. (Tezzeret is notable for being a particularly bad mage, but talented with artifice.) In other words, the only thing that makes a planeswalker different from a normal mage is the ability to enter the Blind Eternities and survive.