You can edit titles on Lemmy! And short answer is no. Even though Musk isn't using the name Twitter for his social media platform, he still owns the rights to the name and the trademark, and can sue anyone using it.
I don't know. X probably still has rights to the Twitter name. Unless they give that up, no one can can themselves Twitter. In fact, why would you can yourself that in an age where that term is associated with nonsensical arguments? It's a form of bias. You might as well try canning yourself Subwoofer instead.
Trademark infringement is a civil matter. If you called your company Twitter, it would be up to the current holder(s) to issue a C&D, lawsuit, etc. If they do not protect their trademark as such, they can lose it. Which would be a very interesting scenario- Musk is very adamant on pushing his favorite letter. This would require them to state in legal filings that they still want and use the name Twitter. Undoubtedly this would hurt Musk's ego, and it's possible that he would force the matter to be dropped.
Also, trademarked names are not absolute. You can use them in contexts where consumers are unlikely to confuse the two. Apple Computer famously had to distance themselves from Apple Records. There's a Dell aluminum siding company near me. There's a Hershey ice cream brand that's unrelated to the famous chocolate company. While it's harder to make the claim when the word is unique nonsense, you could probably get away with a name like Twitter Landscaping.
The new Twitter company could issue a C&D to the old Twitter because they're not actively using the trademark. I don't see why a new company couldn't call themselves twitter if they're willing to go through the court system to take it away.