1: yes
2: yes, there is a Classic mode in Tiger, and lets you start a Classic environment to run programs that require it
3: Don't know about the progs
4: -
If you do Archive and Install it will keep all your data, and install a fresh copy of Tiger, making a 'Previous System' folder where the previous OS will be. It will also migrate all your settings, like users, mail settings, safari...
It is still recommended to make a backup to the external HD. You can use
Carbon Copy Cloner to do this. It allows you to make a bootable backup on the external HD, so you can boot your Mac from it should something go wrong. It will also have all your data and settings/preferences.
With an external backup you can do a 'Clean Install' from the CD/DVD, that will erase the drive and install a fresh copy of TIger. You can then import settings, mail and other from the external HD.
This has been my experience so far, and it has worked for me, but wait for more reply's from people with more expience. Good luck...