I — Tu vois Jean-Paul là-bas ?
— Oui, je lui vois.
correction: Oui, je le vois.
The COD form is "le" for masculine nouns, "la" for feminine
II — As-tu envoyé une lettre à Charlotte ?
— Oui, je la ai envoyé une longue lettre la semaine dernière.
correction: Oui, je lui ai envoyé une longue lettre la semaine dernière.
or
Oui, je lui en ai envoyé une longue la semaine dernière.
"Lui" is the form for the COI and it is used both for the masculine and feminine antecedents. In the second possibility the pronoun "en" stands for "lettre".
III — As-tu regardé la télé hier soir ?
— Non, je ne le ai pas regardée du tout. J’avais trop de devoirs !
correction: — Non, je ne l' ai pas regardée du tout. J’avais trop de devoirs !
The pronoun is really "la", as you supposed, however, before a vowel sound it must have its elided form, which is "l" and it is then separated from the word that follows by an apostrophe.
IV — Parles-tu à tes amis de tes problèmes ?
— Oui, je ai en parle.
correction: Oui, je leur en parle.
Here, the COI plural pronoun is missing; it is the same for all genders and its form is "leur".
There is also an incomprehensible error but the pronoun "en" is right. The tense used in the question is the present, the particular sort being "présent d'habitude"; therefore, if the answer is a confirmation of the action, as the introducing "oui" indicates, the tense must be the same. If the answer had been in the negative, then the tense could have been another one, but then the sentence would not be logical unless ther is a supplement of information (for instance, as in "Non, je leur en ai parlé par le passé mais plus maintenant.").