"He reserves a table for me."
Translation:Lui prenota un tavolo per me.
Yes, tavolo is the piece of furniture, and tavola is the table where you eat. However, for whatever reason, what you reserve in a restaurant is tavolo.
In a restaurant I could say 'Siamo tutti a tavola' (in my caveman grammar), but I would say 'Dobbiamo prenotare un tavolo al ristorante'.
This is a great little article.
mi, not me. Review the Tips and Note in the Clitics-1 module. https://www.duolingo.com/skill/it/Clitic-Pronouns-1
Personal pronoun right before the verb is mi and after the verb is me or a me