Good Morning:
Te quiero hablar and quiero hablarte are the same thing: I want to talk to you
The only difference is where you place the "te" ( means "to you" )object pronoun.
In the first sentence the pronoun is alone, at the beginning, and the verb "querer" conjugated in the 1sr person singular. The verb "hablar" keeps the infinitive form.
In the second example, the pronoun goes to the end of the verb "hablar", and of course, the conjugated part of the verbal structure remains the same
Quiero hablar contigo has the same meaning, but introduces the answer to the question: With whom you want to talk to? Quiero hablar CONTIGO ( with you) / conmigo (with me) con el (with him) con ella, con ellos.
Only contigo and conmigo are one single word.