Here we have an -er verb “étudier”. It’s a regular verb so in the 3rd person singular (Nathalie) we just have to drop the -er and add the ending -e (or basically, just drop the -r and leave the -e) :

Nathalie étudie les maths.

Here we have a regular -er verb “parler”, so in the 3rd person singular (Jérôme) we just drop the -er and add the ending -e :
Parler – il parle

Jérôme parle français.

We have here a regular verb “aimer”. In order to create the present tense, we just drop the -er and add the ending -ons for the 1st person plural.
Nous aim-ons…

Zoé et moi, nous aimons chanter.

We create the present tense of regular -er verbs by dropping the -er and adding different endings for different persons. Here we have the 3rd person plural (Nicolas et Patrick). The ending here is – ent. Ils regardent.. But in this particular case, we as well have the negative form: Ils ne regardent pas.

Nicolas et Patrick ne regardent pas la télé.

Again a regular -er verb “aimer”. In this case, the verb starts with the vowel so we have to drop the -e from “Je”. This is called an “elision”. “Je aime” becomes “J’aime”. Again, we simply drop the -er and add the -e for the 1st person singular. The second verb is in the infinitive form (téléphoner).

J’aime téléphoner à des copains.