1) I bought like 12 domains from various sellers and moved them to a Name.com account, paying for the transfer with my credit card.

I paid the sellers through wire transfer after getting the domain, without using an Escrow service.

After a while, name.com blocked my account and asked me to prove the legality of the domains I bought, saying it was because of complaints they got about these domains.

I sent a scan of my passport and a payment confirmation from my bank, and all my Whois information is correct.

My account is totally blocked, and I can't log in. Name.com keeps giving the same response, like:

"The dоcuments you provided don't prove your genuine acquisition of these domains. Due to the volume and nature of the complaints, the Name.com account will remain closed and the domains set to Compliance Lock. Name.com will follow any US Court Order or UDRP decision to return control of these domains to you. We will wait for the mentioned dоcuments."

Name.com won't say who complained, why, what the complaints are about, or which domains they concern.

Months have passed since I bought them, but the domains are still showing in my panel on Name.com (yes, I can't log in, but I get emails offering to buy these domains + my NS servers are down).

So, the questions are:

Which ICANN email can I use to file a complaint against the registrar?

Where can I check if there are any UDRP lawsuits against my domains?

What can I do, or is this the end?

You're dealing with a frustrating and complex situation. Here's a detailed approach to resolving the issues with Name.com and your domains:

ICANN Complaint: You can file a complaint against the registrar with ICANN if you believe the registrar is not following ICANN's policies. ICANN handles disputes related to registrar behavior and can provide guidance or intervene if necessary. The email address for filing complaints is compliance@icann.org. Be sure to include all relevant details, such as your domain names, a detailed account of the issue, and any correspondence you've had with Name.com.

Check for UDRP (Uniform Domain-Name Dispute-Resolution Policy) Actions: To check if there are any UDRP lawsuits against your domains, you can use the WIPO (World Intellectual Property Organization) and other dispute resolution provider websites. WIPO provides a searchable database of UDRP cases. You can also reach out to the dispute resolution providers directly for information. The WIPO website is WIPO UDRP.

Further Actions:

Contact Name.com: Continue to reach out to Name.com with any additional evidence you have. Ensure your dоcumentation is thorough and includes any relevant transaction details, communication with sellers, and proof of ownership.
Legal Advice: Consult with a legal professional who specializes in domain disputes or intellectual property law. They can provide specific advice based on the details of your case and potentially help in drafting legal dоcuments or negotiating with Name.com.
dоcumentation: Gather and keep detailed records of all transactions, communications, and any other relevant information related to the purchase and transfer of your domains. This can be crucial in resolving disputes and proving your case.
Additional Resources:

Domain Forum: Consider discussing your issue on domain forums or communities where other domain investors or legal experts might offer advice or share similar experiences.
Registrar Authority: If Name.com remains unresponsive or uncooperative, you might need to escalate the issue within the registrar's organization or look for other regulatory bodies that oversee domain registrations.
It's essential to remain persistent and organized throughout this process. By following these steps, you increase your chances of resolving the issue and regaining control of your domains.

Did you made sure to mention the domain names in your payments? And did you send the registrar the docs to prove the payment was made? Like, scans of the payment slips and whatnot?

I purchased a domain using escrow, then flipped it three months later, also using escrow. But three months after that, my client got hit with a TDRP. After another three months of paperwork, VeriSign decided to take the domain back. Since this is a quarrel between registrars, we can't intervene at all.
Now we're tangled up in four different jurisdictions. There's nothing I can do, and now, to save my reputation, I'll have to reimburse the client out of my own pocket. Honestly, it's my fault. I've never been a fan of speculation, especially lowball tactics, but I tried to cash in this time. Looks like TS is facing a similar issue. Usually, when an offer looks too good, something's off. These days, checking domains through whois-history and contacting previous owners is a must before buying.

You can find UDRP claims here: http://www.udrpsearch.com/