Simple question about upgrading with limited available diskspace
 

7.8 GB total diskspace
.5 GB swap
7.3 GB Partition 1
1.3 GB Free Space
256 MB RAM


I am thinking about upgrading from 10.0 to 10.2. First time doing this. Will an upgrade overwrite original system files (and delete unnecessary files?), or is this small amount of free space simply not workable?

If possible, I could downgrade the level of functionality that I get out of the package, in order to make it work.

I'm a little confused. Do you mean your disk is partitioned as follows:
Basically the original figures don't add up, or I'm misinterpreting them. It might be helpful to post the output of
Note that's a lowercase "L".

In any case, doing a clean install rather than an upgrade is what I'd recommend. Assuming you repartition and/or reformat your partitions during the install, then Yes, the existing files will be overwritten. Note that if you don't reformat an existing partition (eg, /home) the data in it will remain as is. What I do when upgrading and/or experimenting with a new distro is to reformat all partitions except /home. In that way, I can install the new distro "around" my /home directory

I would expect the OP means free space within the major partition.

Short answer, it won't be enough. Every upgrade I've seen (especially GUI based) downloads everything first, then proceeds onto the actual upgrade. Usually in a separate environment to the running system.
All adds up to more disk space - which gets released later.