Do Assassin Builds Use Spells?

I'm fairly new to PoE and started a week before Metamorph ended.

I understand that each class starts at a different place on the passive tree but I am not clear if each class gets different values of STR/DEX/INT as they level up?
STR increases your melee attack gem dmg, right? But when I hover over INT it just says that you get more mana and ES; so INT doesn't affect your spell dmg then? And DEX just lets you hit more accurately and evade more?

I keep seeing build titles here and on Youtube that have Assassin + *insert whatever spell*. Does this mean they have viable starter/endgame builds that don't use melee attacks?
Aren't they locked out of buying certain spell gems as well?

Sorry for the noob Q's I'm still trying to figure out so much and what to play before Delerium launches.

All classes get access to all gems, you can buy them from Lily in Act 6 after you complete her quest. A lot of assassins use spells because they scale crits that work with spells as well as attacks but spells tend to be safer. Having more Int means you can more easily equip higher leveled spell gems generally.