LIBERTY'S PROFILE

It depends on the characters. I prefer each to have different ways to learn skills (in RealmS) though in other games it's usually 'level up = skill'. There are also a few field-skills that certain characters gain - some after events or side quests. Most of them are gained by joining a guild of some type - the Cartography Guild, for example, gives Narissa the ability to talk to people officially about areas of interest and allows her to find these areas (and name them after her guild name).

Narissa: Learns via Level Up, skill training (in archery courses) and what quiver she has equipped.
Jidor: Learns via weapon equips. Each weapon has four skills - one auto-learnt and three that need to have 'focus points' put in to them as he levels up. Once a skill is learned he can use it when that weapon is equipped, but if he removes the weapon he can only keep one of the four skills (but can change them at any time).
Clarissa: Mostly training and weapon equipping. I'm thinking about skill advancement where each basic skill can be 'upgraded' to include elemental affinity, status-causers and damage amplifiers.
Mirad: Learns elemental skills by reading scrolls and signing contracts with elemental spirits, though that idea is still being refined. He's the only one that can have magic, but he also has weapon skills. His spells are also enhanced/dehanced by what kind of area he is in - if in a desert fire skills cost less but do more damage, and though ice/water skills may cost more they're more effective against any fire elementals met in such a place (though the fire elementals will also get a boost).

There are also item skills that can be used by all party members and some rare skills that can be gained only through winning duels.

Well, as I said, each character is different, so their ability to learn skills is part of their ability/knowledge/class. Narissa is basically a scout, Jidor a trader/warrior, Clarissa is pole-arm infantry/spy and Mirad a battle magus. Their skills support their characters.

There's a bit of replacement, skill wise, especially with Narissa's quivers, Jidor's weapons, Clarissa's upgrading and Mirad's area enhancements/contracts.

Well there's really not much in the way of overlap with skills, though there are some that may do the same type of things (One of Jidor's skills allows him to divide a healing item among the party to heal at a lower rate, while one of Mirad's skills allows the use of magic to heal low health, but uses base items (think alchemy... sort-of).
Narissa and Mirad have elemental attacks covered, while Clarissa and Jidor cover the de-buff areas. As for buffs, they're usually supplied via equipment, though Narissa has some self-applying buffs and there may be some more in the making.
Mirad is the only mage-type character, though, Narissa is long-range support, Clarissa is mid-short range melee and Jidor short-range melee.

Only certain skills can be learned by each characters. There's no cross-over. Jidor can't learn Archery skills and Narissa can't learn magic. Each skill-type has it's own category, though. Narissa has Shoot (attack), Boost (self-support) and Quiver (elemental/status affliction skills). Jidor has Strike (attack), Swordery* (equipment skills) and Protect (healing/enhancement skills). Clarissa has Stab (attack), Pike Arts (upgradable) and Dare (status affliction). Mirad has Thwack (attack), Arcana (light and dark magics) and Replenish (healing via alchemy).

*Name pending re-evalutation.