df or mount will tell you what is mounted there (I'd guess /home).
In which partitions are all the various folders listed in the file system ie home, usr, bin, etc etc housed.
Most directories are not on a seperate partition. Again, df will tell you what is mounted. Any directory that isn't a seperate mount point is just a normal directory, which will be on whatever partition it's topmost mount point is at. So, if /home is on hda3, then /home/flatstan will also be on hda3. If / is on hda2, then all directories under / that are not themselves mounted partitions will also be on hda2.
For example, my df output is (this is an 80GB drive):
/dev/hda6 192736 135712 57024 71% /
/dev/hda7 256996 103180 153816 41% /var
/dev/hda8 132206 36346 89034 29% /tmp
/dev/hda9 7823376 3197876 4625500 41% /usr
/dev/hda10 61719808 14347688 47372120 24% /data
So, /var, /tmp, /usr and /data have their own partition (note that I have combined /home and /usr/local onto /data). Thus, all other directories under / (except for the virtual filesystems /proc, /sys, /dev/pts etc), are on the / partition, hda6.
When additional programs are installed, in which partitions are they installed to.
It's important to understand that on unix the actual hardware is abstracted away. Unlike other operating systems, which view different drives/partitions as different devices, unix combines all physical drives into a single logical tree starting at / (call "root", and not to be confused with /root, the super user's home directory).
When you install programs, the various parts will go into the relevant directories. So, binaries might go in /usr/bin, libraries in /usr/lib, configuration files in /etc, documentation under /usr/share/doc/<package name> and so on. The fact the /usr, /var etc might be on different partitions is totally irrelevant as far as normal usage is concerned.
I like to use a file sharing program ie eDonkey. On my new
80 HDD I would like to install & use this on a separate partition, I would also like to have a separate partition to use as storage for items, that I do not plan to use for a while, or until I decide what to do with them.
I presume that if I install SuSe on the 80G, accepting the default options, which as a newbie is the surest way of not making mistakes, I will get 3 Partitions as I did (or similar) on my 8G.
I don't know much about SUSE but most auto partitioning utils will use the whole drive by default. You can change the number of partitions and sizes during installation (there is usually an "advanced" or "expert" mode to do this). Alternatively, you could switch to another console and run fdisk/cfdisk, then tell yast to leave the partitions alone.