free tool for number of backlinks and broken links checker

Yes, but you won't be able to export it or anything like that. They'll always be restrictions, reason being, backlink checkers are extremely expensive to run, therefore they need to make their money back through clients paying them money. 

Try webmeup, reasonably good for a "free" version of SpyGlass: https://webmeup.com/

Another option would be a 7-day trial of Ahrefs for $7.

There are many types of free backlink checkers you can use ahrefs.

Here are some free online backlink checker tools that would help for search engine optimization
1. SEMRUSH (Popular)
2. LinkMiner
3. Ahrefs Free Backlink Checker: Recommended for link detox
4. OpenLinkProfiler
5. BuzzSumo
6. Moz Link Explorer

Check the link for creating backlink:

https://www.pitnit.com/article/details/?article=Link-building-in-seo---%22-7-Small-Techniques-To-Create-Backlinks-For-Your-Website-Seo-Ranking%22-78897

Rankwatch is a free backlink generator tool to get a look at how many domains or pages are linking to your website.