Is there a way to limit the available amount of rows and columns?

Limit as you are asking is not possible in the strict sense of limiting.
You would have to either write a macro that they can run to import the data from the customer file and let the macro handle where it goes.
You can also protect the cells the may not be overwritten but then you'll get complaints that the user gets an error message.

Select all is not a good option since select all will select all the 1048576 rows X 16384 columns that is 17,179,869,184 cells

There's already an element of function built into excel, when I hit ctrl-A, it selects all of the area I'm currently working with. If I repeat ctrl-A it THEN selects the entire sheet.

If that doesn't do it, hiding ALL the rows and cols beyond the area you want copied might do it.

If your last used col is H, highlight I, hit ctrl-shift-rightarrow, right click the col labels, select hide.
The space beyond the end of your working area will be background-grey and unusable.
Repeat the process for your unused rows - highlight the first one you don't use, ctrl-shift-downarrow, right click the row header labels, hide.
ctrl-A should now only select the area visible.

I've given this a little test run with a VERY simple spreadsheet, and it works. Something more complex might misbehave, so do test with your own workbook before rolling out to your team.
Any rows/cols hidden within your working area - validations lists, working cells for complex formulae etc will copy along with, but if you're ctrl-A copying you've probably already worked around this - if not, move them to a hidden sheet that's for these ONLY.