I'm a trademark attorney and here are my two cents:
You should consult with a trademark attorney to determine if your desired phrase or trade name would infringe another's trademark. Without knowing the words and doing a proper search, it is impossible for any attorney here to properly answer "yes or no" to your questions. Although you have done a search for federal trademarks, it is still possible that a state or common law trademark exists that is confusingly similar to your desired words or phrase. A trademark attorney could conduct a more thorough search that would more peace of mind.
The fact that it is a non-commercial site is irrelevant for the purposes of trademark infringement. You mention that it is inspired by a popular song, but that should not be an issue because your site is not related to that song. If you site is related to music, that may or may not be an issue.
The trademark and website you found that are similar may be a significant issue for trademark infringement. Trademark infringement is found if there is a likelihood of confusion with another's mark. Even if your trade name or use is not identical, it can still be trademark infringement. Since you mention it is so similar, you must consult with a trademark attorney to determine if you can use the phrase.
With respect to registering a trademark for your domain name, you should first determine whether your use of that domain name or phrase is trademark infringement, as discussed above. If it's not, you could trademark your domain name, but the first mark you want to register is the name of your company, non-profit entity, or name of your website. Registration of your domain name should be secondary since nobody will try to use your domain name on their materials; that would just send traffic to your site.
Finally, I don't think you should share your domain name here. It will forever show up in search engine results, which may be awkward for you. It will also give others who want to challenge your mark ammunition because they could claim that you willfully infringed after posting the mark on a legal website specifically asking for advice regarding trademark infringement.
I hope this helps. You can contact me if you want to discuss this matter further. You should absolutely discuss this matter with a trademark attorney before you proceed.
This answer is for informational purposes only and does not create an attorney-client relationship between us.
I agree with the previous post. It is difficult to ascertain whether you will have a problem based upon the information you have provided. You have indicated that you have performed a word search for the trademark using the Tess system at the USPTO. My suggestion would be to do individual word searches for each word used. You might also want to try different spellings of the words.
As the previous post mentioned, it is probably not wise to reveal the name at this time. You might be able to find an online service to research any potential trademark violations but they may just do the simple word search you undertook.
It appears that you have also done a google search. If not, I highly recommend it at this time. You can have a trademark without registering it.
I hope this was helpful.
Trademark is a grant from the government to exclude others from using a word or mark to denote the source of goods or service. It is not a right TO USE the phrase, it is a right to EXCLUDE others from using the word or mark.
If you don't ever plan on using your site to sell goods or services, you cannot register a trademark for your domain name.
TESS is for federally registered marks, it is not necessary to register your mark to gain trademark rights, but registering your mark grants you additional rights. States can also register marks.
If you are worried about getting sued for using a word in your domain, no one can every tell you, you will never get sued. Anyone can sue for anything, whether or not they will win is a different matter.
It would be a good idea to get a trademark attorney to go a search for you to give you an opinion of the likelihood your mark infringes on the rights of another. But that opinion will not include a guarantee you will not ever be sued.