@aristotle has it exactly right about what a brand is - it is a "Name, term, design, symbol, or any other feature that identifies one seller's good or service as distinct from those of other sellers."
The OP forgets that the job of a search engine like Google is to return the most RELEVANT search results to a query.
They are not, and never have been designed to rank businesses by which has the most limp-wristed social media consultant.
1-A Twitter account that's more than links from contents from your site where you are involved in a discussion with the public.
Twitter accounts busy with many @replies bore me immensely. Why is this good for a search result?
2-A Facebook Web site with original contents not found on the main site, or contents that offers value added benefits that users would not find on the original Web property - a site that goes beyond just hosting a message board and answering users' questions.
Why would Google reward a site where instead of just having the information on the website, you have to have an account on a third party site and leave to find it there? What has inane social activity got to do with the relevancy of search results to my query?
3-A real distinctive visual identity that can exist outside of the Web.
"Acme's new logo is soooooo last year, down to page two for them!"
Apps are trendy so they have to be mentioned. I think apples would be just as effective a metric. Whichever site has the most apples wins.
5-A Physical newsletter, or similar contents available as printed material and sold on offline networks.
If this was implemented as a ranking factor by Google the amount of waste paper generated would hasten the planet's deforestation problems.
6-Custom gear, props, with your brand.
I can't wait until Google launches their "Apparel algorithm" and every business brings out a range of t-shirts, ties etc to get ahead in the rankings. Marketing consultants can choose the Autumn range instead of doing real work requiring knowledge.
7-Participation in an industry or a public event like a local festival, not only as a sponsor, but as a guest/speaker.
If this was the case, search results would be a buyable popularity contest. (...)
8-Offline third party recognition, references. For example quotes from a local newspaper on an article where they interviewed you on a specific topic
Google already indexes content from local newspapers that are online. If it's not online, chances are it's not a noteworthy source.
9-An endowment or prize under your property's.
Under your property's what?
10-Mix media contents, like a podcast, a YouTube channel show, or a cable show.
Porpoises would be just as good a metric as podcasts. If you don't have a photo of a porpoise on your homepage, you aren't part of the trendy club and you can't rank in search!