apt-get
installs things wherever the packages say they want to be installed. This is typically somewhere in /usr
and /lib
.
Reinstalling can be done in a variety of methods. If you install over the top of an existing installation, you probably won't have to reinstall applications but you may have problems with dependencies. The reinstalled version of Ubuntu won't know that some things are already installed.
For that reason, a clean install is usually recommended, in which yes, you will need to reinstall your applications, just as you would with Windows.
I personally don't keep /home/
on a separate partition. This is more due to hardware (a small but stupidly fast SSD as my root partition and terabytes of slow RAID5) than anything else but I just keep the stuff I really want to keep (documents/music/etc) bind-mounted on the RAID5 array and then backup things I want running fast (firefox profile, etc) on a regular basis.
I don't think there's a single best answer for every user but if you need more disk space for applications, you need a bigger root partition. That much is pretty simple.