The conjugations of the infinitive mettre in present tense:
Je --> mets
Tu --> mets
Il/Elle/On --> met
Vous --> mettez
Nous --> mettons
Ils/Elles --> mettent
Answer:
1. Nous mettons nos chaussures.
For question two, remember that Marc is a singular male, thus, you'd use the conjugation for il.
2. Marc met ses chaussures.
Quick tip: In my experience all infinitives conjugated for the subject nous end in -ons; likewise all infinitives conjugated for the subject vous end in -ez. Due to this, it was immediately evident that the correct answer for question one is not listed here.