1. Don't mention where this is the original timeline, the Abrams timeline or a new one until the final episode of the first season.
Well, in either timeline they should set it post-TNG era, simply to be able to use common Trek lore like replicators, the holodeck, the Borg or the Ferengi.
That being said, the show should have a modern, completely unique own look and feel to it. They should give us the timeframe of the show very low-key (for example by mentioning "a message from Vulcan", or "Admiral Janeway's lecture on the Borg" in the background), so that for casual viewers it could be interpreted as a continuation of both the original timeline or the new movies.
2. Include relatives of known characters in the show--but maybe don't make immediately clear their exact status. For example, we might have an officer named "Kirk" onboard.
I don't know, feels kind of forced. I prefer giving us a straight up cameo of an old character during a Starfleet meeting (but DON'T write an episode around an old guest star! At least not during the first two seasons!)
3. Throw in a wild card absolutely nobody will expect--such as the Borg treated as trusted allies of the Federation!
YES!
Although in this case, I wouldn't take the Borg (they are too unique in all of pop culture. Transform them! But keep them as adversaries). But how about we casually have an ambassador who is a shapeshifter?
4. Do a redesign of the basic Starfleet shape, echoing what we know but taking it in a new direction (a vertical orientation for example, or a very different color scheme).
Hm... not sure about that. The Starfleet shape is an iconic look as much as the Bat Symbol or Supermans' chest. Modify it, for sure! But keep the basic shape.
5. Please make the series 'antagonists' something that resembles Al Qaeda and/or ISIS not even a little bit.
Well. Don't do it "on the nose". But why not let them have the same general effects? When the Borg first appeared, suddenly everyone was a target, not just one's military, but all of population as well! That was a pretty big game changer, and would allow for stories that are identifiable in the modern age. Don't make the villains barbaric terrorists from a desert planet. But let them have the same effect (EVERYONE could be a target now!) on society.
6. A genuinely interesting Captain/First Officer combo. Frankly the re-imagined BSG and Joss Whedon's Firefly did a much better job than almost any Trek since the original.
The Captain/Doctor combo is one not to be despised as well

It's the only combination where no one "outranks" the other, so there could be genuine friendship easier (a lot of naval books have that combination!)
Just make sure the characters are new and interesting, and not a rehash of the Kirk-Spock-McCoy trio!
7. An idea to explore--the Federation consists of such a huge array of cultures, Starfleet itself must function as its own culture at some point in order to work. This means there are likely families that routinely join Starfleet, and certain types of dissidents made welcome there (refugees, half-breeds of races that don't get along, certain dissenters such as emotional Vulcans, etc.)
Yes AND No.
I would love to see more characters stepping out of the norm (emotional Vulcans, honourable Romulans, philantropic Ferengi and peaceful Borg).
But I don't want essays about Federation Society. A good backstory is welcome, but Star Trek should be about the adventures out there. Whenever someone tries to show too much of human society, it becomes less of an interesting story, and more about a (boring) predicion of the future, which will probably be rendered irrelevant in less than ten years anyway...
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