You need to re-install applications because they are installed to the root
file system. Home is for settings and data. The only way to get around that
is to upgrade and even then it will likely upgrade most packages as well
because of newer versions. In the future Ubuntu will have a delta system
where it will only download the difference between old and new. We are not
there yet. Fedora 12 has this feature with Presto enabled Packagekit. It is
something being considered I believe, but not implemented.

What I do is save a list of my installed programmes to a text file and then
have apt install the packages from the text file. This still involves
downloading however, if that is the issue. I am not sure if it is your
connection or just the idea of having the old new system resemble the old.
If it is the latter then the text file will serve you well. I can tell you
how to do this if it is your preference.

As for saving home, it all depends on what resources you have available. If
you have a big enough drive then you can just re-partition and copy
everything to the other partition. Or if you have external drives or usb
sticks you can copy to it. Otherwise you must burn individual files and
folders to DVDs. From your layout I can see drive size but not know how full
they are. If the NTFS drive has enough room you could copy home to it. Then
move it back later. That would be the easiest solution.

If you are like most people you are probably running without much extra
space and that means that we would have to look at other solutions. If you
copy individual files and folders be careful to enable hidden files because
most settings are in the hidden folders.