How much disc space do the exports use?

Flat nodes don't impact upgradability but their benefit is greatest for full planet imports.

Since you do not need a continuously running tile server - you can afford downtimes while updating - the most space-efficient way to do what you want is

1. if your area of interest is rectangular, goto 2; else determine the area you want and create a "poly" file for it (e.g. draw polygon in josm, save as .osm, use osm2poly.pl - or use another method)
2. download europe-latest.osm.pbf from Geofabrik
3. use osmosis (or osmcut or osm-history-splitter) to cut out the area of interest from the Europe file
4. import the resulting file with osm2pgsql using the --slim and --drop options which leads to a non-updatable database and makes the database unusable during import
5. whenever you want to update, repeat steps 1-4.

Alternatively, if you do want uninterrupted service, follow steps 1-3 above and then

1. import the resulting file with osm2pgsql using --slim
2. when you want to update, repeat steps 1-3 above and then
3. use osmosis with the --derive-change option to compute the difference between the new file of interest and the last one and save to an .osc file
4. use osm2pgsql with --append to load that .osc file

There are other options, like consuming the Europe diffs from the Geofabrik site, but that would lead to unnecessary data in your database that you would have to remove from time to time.

In answer to "How much disc space would I need for ① ?", I suspect that 300Gb would be a bit low, currently. I don't have a Europe extract maintained currently, but when I last did (a couple of years ago) my recollection is that it needed 250-300Gb, so the requirement would be larger now.

However, I'm sure that someone must have more up to date figures.

At the start of this you say "I need to have a local tile server set up because you guys block MOBAC, and I need offline maps for geocaching.".

I'm guessing that the issue here is lack of data coverage and cost of mobile data when you're out and about.

However, maybe it's worth taking a step back and asking if lots of individual map tiles is the best way to hold and display data? I don't know what you're displaying data on, but if it's a phone there are quite a few options (Osmand's offline layer may work for you if you're using an Android phone, and plenty of other options are available).