Airtable is not an app-building tool. It is a spreadsheet with some very basic database features built into it. It won’t natively do everything you want to do.
You could embed your Airtable base on your website and allow people to export it as a CSV file. They could also search/filter your records, They could print what they see onscreen, and they can use their operating system to turn the print job into a PDF file.
Anything beyond that, and you’d need to piece together other apps & websites to communicate with Airtable via Airtable’s API, or via Zapier/Integromat.