How responsive is 2012? – Webmaster Tools errors

This is a beginners question. I’m confused about responsiveness.

BACKGROUND: I need both my 2 small, text-based sites to be adequately responsive on ipads and big mobiles. They don’t need to look perfect. These are not sites people read in depth on small mobiles. So if the responsiveness is poorer on small mobiles, that is not a big problem. What is VERY important, is NO error messages about responsiveness from Google Webmaster Tools!

My older site is developer-made on a 2012 child theme. This did cause Webmaster Tools errors complaining that what I was showing to mobiles was not responsive. So, I’ve ended up with a separate “ghost” site, highly responsive, of just a few main landing pages. This is shown just to small mobiles. Everyone else, ie laptops, ipads, big mobiles, get shown the 2012 child theme. This is a bit weird, but, as long as it works, I am not going to change it – better things to do.

QUESTIONS: (1) About the past – Is this ghost site for small mobiles necessary? Is 2012 really not responsive for small mobiles? Is there some other way to get rid of the GWT error messages without a ghost site?

(2) About the future: I now want to create a small, new text-based site which has no developer input, no child theme, and is very simple. As above, it needs to be reasonably responsive, and NO GMT errors. If I make the site in 2012, how responsive will it be? Is 2015 more responsive? Will either eliminate errors? If 2012 is not sufficiently responsive to prevent errors, is there another theme which looks like it?

Many thanks

Andrew