Ist weitermachen ein Wort, das nur für Menschen benutzt wird? Wird weitergehen auf die gleiche Weise für z. B. eine Ausstellung benutzt?
The part "weiter-" means: "To continue to do something".
Example: "weiterschlafen" means: "To continue to sleep".
This can be done with most verbs.
The verb "machen" (in this context) means: "To do something".
So the verb "weitermachen" means: "To continue to do something".
The verb "gehen" has a lot of meanings. In the context of an event it often means: "To take place".
So "weitergehen" (in this context) means: "To continue to take place".
This is about the different translations of the English verb to continue, I guess.
Das Konzert geht weiter.
The concert continues.
Wir machen mit dem Konzert weiter.
We continue with the concert.
There's a change of the subject. In the first sentence, it's the concert which does something. In the second, it's we.
As you found out already, weitergehen in the meaning to continue can only be applied to things. When applied to persons, it means to continue walking specifically, which is not what you meant.
Es geht weiter.
It continues. ("Es" is an event or similar thing.)
"It" continues walking. ("Es" is a person or anything with legs to walk, but the noun used is of the neuter class, e.g. das Mädchen.)
Sie geht weiter.
"She" continues. ("Sie" is an event or similar thing, but the noun is of the female class, e.g. die Tagung.)
She continues walking. ("Sie" is a person or anything with legs to walk.)
(If you wonder how comes "Sie" can be a thing, remember German "genders" are only noun classes and have no meaning on top of this.)