With Velo code, is it possible to add new fields (including text) to items in a database?

No this is surely not what you want!!!

Better way → using either…

a) ARRAY-FIELDS
…or even better, using…
b) OBJECT-FIELDS

This way you can store for each of ROW (LINE) all messages related to a USER.

You surely don’t want to create an infinite DATABASE creating infinite COLUMNS!!!

Your issue has a lot of similarity to the following…

At the end you also can create a second database → for MESSAGES <— and include them in your QUERY…

https://www.wix.com/velo/reference/wix-data/wixdataquery/include