Which should I connect if I use both a store and Stripe?
Both, for different tables. The store knows orders, products and who bought what. Stripe knows subscriptions, invoices and payments, including any that never went through the store, and it names each customer by email address. Import what each one is the authority on, rather than the same customers twice.
Do new orders appear by themselves?
They can, on a schedule. Importing again adds new orders to the same table and updates changed ones, matched on the store's or Stripe's own IDs, and Keep in sync runs that hourly or daily for each connection. A Shopify store without the wider order permission only ever shows an import the last 60 days. Work that has to start the moment somebody checks out needs something that listens, and an import doesn't.
What does the WooCommerce connection need?
Your shop's address, which must start with https, and a REST API key made in WordPress under WooCommerce, then Settings, then Advanced, then REST API. Read permission is enough, because RowFold only reads from Woo. Paste the consumer key and the consumer secret, which WordPress shows once, and press Save & verify.
Why are some WooCommerce customers missing?
Guest checkouts aren't customers in WooCommerce's sense: only people with an account on the shop appear in its customer list, and the import brings that list. Guest orders still come across in the orders table, with the buyer's name and email on each order, so nobody's order is lost.
Can RowFold change anything in my store?
Only through actions you put in an automation. Shopify can adjust a product's stock level, and Stripe can create a payment link or a customer. WooCommerce is read-only. Imports never write back to any of them, so importing can't change an order, a price or a customer record.