Unix user alias

No, unless the Solaris box in question have been setup in a rather exotic/strange way there are no way for you to specify a public key to use.

Assuming we are talking about the usual scp client, which is part of OpenSSH, it in itself won't accept a password non-interactively.

One solution might be to write your own scp "client". That is, put something together in your favorite scripting language, using a suitable module/library, allowing the password to be inserted non-interactively.

Don't give them root. Give them an individual account and place it in sudoers. Every command they launch with sudo will be put into the log. However, sudo power still allows them to clean up the log, and to log in as root with sudo su -.

The solution is to have the log segregated on another server, with something like syslog-ng. They can turn it off, but their having done so will be recorded and should be a great big red flag. As will su -. I'm guessing you can block that in sudoers with a bit of thought.