That is something that may most probably be solved with a simple css using media queries, or maybe a pure responsive css style. Sadly it’s allways my last priority cause of my personal dislike for playing IF in a mobile phone (too small for my patience). I’ll have a look at that anyway, it’s not what I like, it should be what player like 
Correctly-designed web pages should look fine on both desktop and mobile, and they should respond adequately to changing the font size (usually because all sizes should be specified in vws or rems). Prospero for example fulfils those requirements, though it wasn’t targeted at devices with extremely small screens – the baseline I use is a first-gen Moto G, which is a lower end device with a small screen.
You can’t really tailor a web interface to specific devices reliably, but you can tailor it to specific screen sizes (and to touch versus desktop interfaces), which should be enough.
Hear hear. But again, the more customization the actual game provides, the better. Because, well, you’d think that all web browsers today allow you to change font size, right? But the browser I have to use to play them on my small iOS device doesn’t, not for web pages that I’m opening from local storage. Just goes to show you can’t anything for granted!
I do think that you’ll generally get the best experience with a tool made to play IF compared to a webpage, although webpage does have certain benefits as well.