Will my numbers change on install? No. Each stock managed product gets a row in the default location with its current quantity.
What if I remove the plugin? WooCommerce keeps its totals. Location data stays unless you ticked removal in Advanced.
Does it change prices or tax by location? No. This plugin is about stock and fulfilment.
Direct database writes. A plugin that writes to the stock field without WooCommerce is not seen until you run the Tools check.
Point of sale. POS and ERP systems can use the REST routes. No POS is built in.