Is there a limit to how many files my customers can attach to a ticket through the web form?
There is not a limit on the number of attachments for authenticated end-users, but rather on the size of the attachment. The web form utilizes linked attachments and as such, the size limitation for a single file is 50 MB, as described in this section: Attachment size limitations.
Unauthenticated end-users have a hard code limit of five attachments for each web form request as a spam prevention policy.
For related information, see this article: Can I change the attachment size limit in ticket comments?