"Querer" is a great example of a word that doesn't have a precise equivalent in English. In the Latin American environments I've been in, people rarely used "amar", which translates most closely to "to love". But "querer" can express an intense emotion as well. If someone says, "Te quiero mucho," there's not necessarily any cap on the feeling, the way there is, for example, in French, with the expression "Je t'aime bien."
No, the "a mí" part is completely optional and just emphasises the me in front of the verb.
"Tú no me quieres" can be translated as "You don't want me", but when you're talking about two people, "love" is the likelier interpretation of querer. If you want to specifically go for "want", you can use desear ("desire") or apetecer (cognate with "appetite").
Object pronouns usually come before the conjugated verb:
Objects pronouns can also be attached to: an infinitive (if there are two verbs), a gerund or positive imperative (with the last one it’s obligatory):
- Lo voy a hacer. = Voy a hacerlo.
Te quiero decir algo. = Quiero decirte algo.
- Le estoy escribiendo. = Estoy escribiéndole.
- Hazlo. Dámelo. Cómpralo. Dime.