Upgrading Drupal

While upgrading my personal website from Drupal 6.2 to Drupal 6.3 I hit the 16MB memory barrier. My ISP does not allow more memory for PHP hence I'm a bit stuck now. The error I see when I try to run update.php is:

Fatal error: Allowed memory size of 16777216 bytes exhausted (tried to allocate 453 bytes) in /customers/shutterfreak.net/shutterfreak.net/httpd.www/includes/database.mysql-common.inc on line 35

Is there a way for me to perform the required update statements in smaller steps?

I upgraded my drupal site from 6.2 to 6.3, and ran update.php and got no errors. But when I tried to access admin (after login as admin), it lags and displays the server not responding error. I can access the site fine, and content loads as fast as before, but I can't access admin. Any ideas?

The security alert telling me to upgrade drupal gives the following message:

Includes: Aggregator, Block, Color, Comment, Database logging, Filter, Garland, Help, Menu, Node, Path, Statistics, Syslog, System, Taxonomy, Tracker, Update status, Upload, User

Does this mean I really only need to overwrite these modules with the new versions of them? Do I need to overwrite everything, or just these modules?

I guess you could call me "intermediate" as far as experience with the front page module goes.
I was looking for something that could tweak the regular menu in zen_classic to eventually be more "graphical".
(i.e. rollover a shape instead of a button).
I knew I probably wanted to tweak the front page code. I popped in the front page module, cut and pasted the source from
my current front page and set the default front page to "front_page".

I tweaked a button on the front page to test it.

What is the easiest way to upgrade from 6.2 to 6.3?

The upgrade.txt looks too complicated!...

Is it ok to just upload the 6.3 overtop of my existing, and then run
the upgrade.php?

I have quite a few sites, none of them are overly complicated.

Help, I've just upgraded Drupal to 5.7, followed the instructions and ran the upgrade.php and now my site seems to have some additional text in the default URL.

it's gone from www.example.com to www.example.com/pub-cgi/

and therefore nothing on the site seems to work... if I delete the /pub-cgi/ part of the URL I get to see something - which doesn't look good, but does give me links to other parts of the site - where all these links also include the /pub-cgi/