Your first question. If it's an rpm, it doesn't matter which directory you install from. You can then hold on to it or dispose of it depending on your wishes. For .tar.gz files, it's OK to untar them in your home directory. It's more standard to untar them in a subdirectory of /usr/src. Then once you've finished installing it, it's a good idea to compress the source and store it (in /usr/src). That way you can do a make uninstall if ever you wish to get rid of the program. Otherwise it tends to get messy with compile-from-source apps.
Your second question is what people call "dependency hell". Mandrake, I believe, has a dependency checking program. It's called urpmi or something like that. I don't use mandrake so I don't know anything about it but try to use that. There is also a port of the debian app apt-get. Have a look around google/linux and sourceforge for it. If urpmi doesn't do it for you, it's well worth investing a few days to a week to get apt4rpm installed and working. It will save you from dependency hell. If you don't want to do the above, you'll need to download every dependency individually and install them simultaneously.