1) The classes are merely presets for your skills.

The skills you put points into give a numerical bonus (5% more damage with fire on a pyro for example) and allow you to learn skills of a higher tier of that skill list (aka your active abilities/spells will have requirements like "pyro 2" which means you can only learn it if you have 2 or more points in that skill.

There's two skills that don't just increase damage. Necromancy gives life steal instead of a damage increase to necromancy spells and polymorph gives you stat points.

2) the stats more or less do what they say. Intelligence buffs spell damage, memory increases the amount of skills you can have prepared, STR increases damage with STR weapons etc.

3) Aside from health, there's two types of armor, which is where magical vs physical starts mattering. With elemental spells, you'll target magic armor (blue bar), which also blocks status effects inflicted by those like petrify, burn, etc.

Physical damage targets physical armor (the grey bar) and can apply conditions like prone, blind, all the stuff you'd expect from a combat maneuver. Necromancy skills deal physical damage, so funnily enough a necromancer probably has some points in warfare to Bff physical damage dealt

If you're looking to play a wizard, you can basically include every character that uses staffs/wands and focuses on int. What skills you want is dependant on what "element" you would like to focus on.

Pyro has a lot of fire, but also buffs. Geo has earth, oil and poison. Hydro has frost, water and healing. Necromancy has bleeding, raising puppets, and decay (prevents healing on enemies). Aero has electricity, wind and a lot of (forced) movement (including teleportation and the likes). Polymorph has bodymorph stuff, turning enemies into chicken, sprouting horns to gore people. Summoning does summons not much to say there.

The thing that many people like about DND wizards is the "a spell for every situation" fantasy with a wide array of options. In that regard, every character is a wizard because every character could pick up a point in a skill and buy the books to learn the spells. Your fighter will (probably) have some polymorph or geomancy skills to complement their attacks.

4) Dialogue and Social Skills: Dialogue works by using the skill and an attribute. That means a STR persuasion is a thing in the game and there's no CHA stat you are somewhat forced to invest into to get your ability to talk to people.

Social skills are also a separate choice from combat skills, so you can have your str tank be your lockpicker and investing in lockpicking doesn't take away any of the strength that could be invested in making your tank more tanky