Google Webmaster Tools is now called Google Search Console

For keyword research I like Ahrefs, for site audits I like SEMRush.

I would delete the post and give them a warning, 2nd offence would ban the profile. Maybe they would contribute in a more positive way in the future.

Some of those sites might increase their power over time, if so the link would be even better for you.

What keywords are you trying to rank better than them, are they included in your home page title tag?

It is better to have blog posts within your own domain rather than a subdomain.