I am interested in starting a dropshipping store and I was wondering if I could do it with only a paypal account. Please help, thanks.
Nick here from Shopify.
Great questions! You can indeed use your own domain during the 14-day free trial. I would highly suggest double checking and making sure you would want to continue on and purchase a plan by the stage you want to add your own domain for the main reason that removing the domain from a closed down store or a store without a plan can be a nuisance. Something else to note is that it can take up to 48 hours for a custom domain to point to your store. Generally, it doesn't take that long, but it is something to be aware of with the trial only being 14 days. Shopify has a great guide and information document going through all the steps for how to add a domain to your store which you can see here.
Regarding your question about having PayPal as your only payment gateway, that is no problem at all. One thing to be aware of is that to use PayPal as a payment gateway on Shopify, your PayPal account needs to be a business account. Once set up though, you wouldn't need to have any other payment gateways should you not wish to. Shopify also has a guide going through all the steps to set up PayPal on your store that you can find here.
Hope this helps!
All the best, Nick