1> There is no proper free tool for Backlink Analysis.
2> You can use Ahrefs for Backlink Analysis you can use any group buy service to purchase it in reasonable rates. You can also get trial of Ahrefs for 7 days for free.
3> Yes you can use Google Disavow tool to remove spam links there is no limit to use it.
4> There is no fix quantity for making backlinks but make sure you don’t spam. Many experts suggest to make 7-10 backlinks daily and yes maintain dofollow & nofollow backlink ratio to 1:2