How can I download and access the lat/long and title of every park in the USA?

You can start with this 7 GB file http://download.geofabrik.de/north-america/us-latest.osm.pbf and then import that into a PostGIS database with the osm2pgsql utility. On import, you can provide a "style file" that says which objects you are interested in; if you use this to limit the import to features of interest - at first guess, probably "boundary" polygons you you can find out which city or state something is in, and "leisure" polygons so get the parks - then you should end up with a relatively slim database. Be sure to use the options --slim and --drop on import to save space, and use --hstore to ensure you have access to all tags you need. An even more surgical option would be pre-filtering the PBF file with the osmosis utility where you can not only specify keys but also key-value combinations that you want to import, yielding a much smaller PBF file to feed to osm2pgsql.

Be aware that the word "park" means many different things - anything between "a patch of green in the city" and "a state-sized highly protected natural reserve", and you might have to invest a little time to get the queries right. See the discussion starting at https://lists.openstreetmap.org/pipermail/talk-us/2018-January/018263.html for some background.