If I purchase a refurbished MacBook Air, can I schedule to bring it to my Apple Store to have data tranferred from old MacBook Pro?

I sure they would help you, call them to verify.

From iOS device using the app to make a online Genius Bar appointment is easy:

https://itunes.apple.com/us/app/apple-support/id1130498044?mt=8

(note: due to the temporary closure of Apple Stores and the staggered reopening there may be some delays.

ref: https://www.apple.com/shop/browse/store/temporary_closures )

The most trouble free way is using the Setup Assistant on the initial boot— you have one shot here.

https://support.apple.com/en-us/HT205749

If that opportunity has past, the second best way is use the Migration Assistant.

How to move your content to a new Mac https://support.apple.com/en-us/HT204350

You may need the adapter for mac with thunderbolt only

USB-C to USB Adapter - Apple

The last time I swapped over from an old device to a new device, there was a table in the back of the store designated the device upgraders table, for Macs, iPads, and iPhones.

They had a collection of adapters and cables that might be needed to make the conversion, and a knowledgeable and helpful Apple employee (Camp Counselor) there to help you with your project. (shared among the half- dozen upgraders who were there).

¿Do it for you? -- They were not really willing to do that, but if you were not savvy, they could provide a LOT of help.

+1 on checking first.

In the non-COVID world they used to do that.

IN the COVID world with so many people working and studying from home, store, all tech companies' support groups are hammered with support requests.