Disclaimer: I've done work in the past with one of the founders on a former iteration of this product.
2. I don't think you need to restrict yourself in order to constrain yourselves as long as you consider features in a "will this work well on mobile" mindset.
3. I disagree that mobile is a more open playing field. What exactly is your barrier with a browser on my computer vs. a browser on my smaller (phone) computer? Perhaps I misunderstand, but this doesn't make any sense to me.
Glad to hear you'll be adding a web component. As I mentioned elsewhere, I'd also suggest you allow users to try the thing before requiring them to download and login - especially with Facebook, but even without. Service sites like Zillow generally do this well.