Laid off, Cobra paperwork never sent. Department of Labor fines?

I got swept up in a mass layoff in mid-May. After that, my ex-employer did basically nothing. I had to harass them for my severance doc to sign, to return my laptop, etc. They still had me listed as an active employee three weeks later so I called ADP, which handles payroll and benefits, and they followed up with my former employer to get my status updated. At that point they (ADP) said there would be Cobra packet coming. That never happened. The 30 days +15 days notice period ended the end of June. My family and I do not currently have health insurance. We were counting on using the 60 day Cobra enrollment period (ends end of July) for retroactive coverage in anything happened between now and then, and buying our own insurance from the marketplace starting Aug 1st. Obviously, we can’t do that without any info on Cobra.

I’ve contacted the Department of Labor who’s attempted to follow up with my former employer but hasn’t received a reply. I’m getting annoyed that they are in violation and are not yet being fined. The fines are trivial as well. My questions are:

Who is fined, my former employer, or ADP? Who are those fines paid out to, the government or me? If I don’t get my Cobra info before the end of my 60 days, what happens after that? Can I go after my former employer for medical expenses, including the insurance I’d have to buy? Anything else I should know about this situation?