I will create a PHP based crawler

This script can be execute directly from your PC if you have installed XAMPP/WAMP server, otherwise it will execute directly if you place it at your hosting server.

Script can fetch thousands of pages if your server allows, you will have to increase the execution period according to your requirement and get a suitable hosting plan accordingly.

Yes, this is possible at additional cost since a customized Apps Script would be required to make a communication link between the PHP script and Google Spreadsheet.

This depends upon specific requirements, usually it will use simple CURL, Multi-Curl, Multi-Threading, Symfony, Rolling-Curl and few more libraries for fetching information from target websites.

Yes, the scraper can login and perform basic level actions like clicking buttons, typing information in input fields & submitting forms. This feature isn't available in simple/medium level gigs, consult before ordering.