Getting some social proof is a great idea. I have some author friends in real life, so maybe having endorsements from them on social media will help instill confidence. I think the first few months will be the hardest, but eventually we'll have a track record.
No, don't do that. Writers do not need social media endorsements for publishers. Show yourself and if you are new in the field then what's your roadmap? Have you raised any funds? If yes, how and if no then how you'll pay. Your website has only two pags mentioning nothing about you at all. If your website is hosted on a shared-hosting then it'll be taken down by your "human and bot" visitors collectively after publishing your first issue.
Precisely, tell writers your raodmap so a trust bond can be created between you (as a publisher) and writer. Do you agree?
Just creating an 'About Us' page with some info on who you guys are would help. Currently the site is pretty much a faceless oblivion.
Don't get me wrong, I like the concept, and would be interested in writing for you to get my name out there, but as others note, losing control of our work is a huge fear - if we as writers willingly submit our work into a black hole, that's it.