Can I use a GPS from old Garmin with an Arduino?
The short answer is NO, unless you have solid experience with microelectronics.

Finding documentation for a module you take out of a commercial device is hard to impossible. Chances are, that module is specific to Garmin, and even if it isn't, it's certainly EOL by now, with no support whatsoever.

Even if you do find the spec, there is a high chance that you'll have to write a software library to support it on Arduino. Don't expect the supplier to share the code they gave to Garmin.

Finally, to put together and debug this project, you will need quite some equipment:


oscilloscope to debug the electrical interface
soldering station to solder small pins properly


Like people said in comments, this equipment alone will cost much more than a brand-new GPS receiver.