Can source tarballs be installed in Linspire with the commands configure, make, and make install from a root terminal?

Will autopackages work in Linspire? I know autopackages are supposed to work in each distro, but Linspire is a special one, and I do not know if that includes Linspire.

I don't have linspire, but I don't see why you wouldn't be able to install from a source tarball.
Installing by a tarball will, by default, install the software under /usr/local. This sub-hierarchy is supposed to be untouched by the distro, even if you reinstall (provided you don't format the /usr/local partition when re-installing).
Of course, there are some prerequisites you will need such as installing tar, autoconf, the gcc compiler, and possibly others that are needed by all standard tarballs. Also, one tarball may have it's own dependencies.

I've run into a problem once where a tool that was needed to install wasn't found. My mistake was running the "make" part as root, when I should have run it as a normal user. But using Linspire, perhaps you don't have a choice and always run as root. This only happened to me once. I'll often produce documentation from the source rpm (in /usr/src/packages/BUILD directory) as root without problems.

It is alway worth a try. The first ./configure phase will probably fail if there would be a problem. The configure script examines your system and performs tests before writing a Makefile. If the makefile is produces successfully, things will probably work OK.

For the other part of your questioin, you may need to install and configure a packaging system or frontend before using something like YaST, urpmi or whatever the packaging managers for a debian system are called. Not knowing much about Linspire, I won't go further and blindly lead you astray.

Good Luck.

Will I need build-essential to compile and install from tarballs on Linspire. Does Linspire come with everything I need already to compile and install from source tarballs? No matter how hard I try, and I have spent lots of time trying, I can not get tarballs to compile and install. I have tried suggestions including having dev packages and build essential. My error is about OpenAL now, and I already have that with it's dev package too. Nothing is working, so I may give up at that. Some software is only available in source tarballs.

Unfortunatly not. Linspire has decided to not include the development tools in it's base installation. (from a security standpoint it's a good thing since you can't compile a rootkit if you don't have make on the system, but it's anoying as hell for more advanced users).
What you will need to do is to install (prefered method is through CNR but APT might also work) the development tools (there is a special Developer Aisle in CNR that contains ALL the software the developers at Linspire use to build their programs so it should have everything you need to compile most source tarballs).

Again, installing Source Tarballs, with APT, ... is not officially supported by Linspire.