> What if I decide to offer that script as a service for free to friends and family, who can use my cloud server?
You're allowed to make copies and adaptations in order to utilize the program (website), which probably covers a cloud server you yourself are controlling. You aren't allowed to do other things with those copies though, like distribute them to other people.
Payment only matters if we're getting into "free use" arguments, and I don't think any really apply here.
I think you're probably already in trouble with just offering it to family and friends, but if you take the next step offering it to the public that adds more issues because the copyright act includes definitions like "To perform or display a work “publicly” means (1) to perform or display it at a place open to the public or at any place where a substantial number of persons outside of a normal circle of a family and its social acquaintances is gathered; or (2) to transmit or otherwise communicate a performance or display of the work to a place specified by clause (1) or to the public, by means of any device or process, whether the members of the public capable of receiving the performance or display receive it in the same place or in separate places and at the same time or at different times."