Various problems after the update.

i added the snippet in the theme i use for amp pages (twenty fourtree) and now it seems that everything is back to normal.

As a short term fix, editing Twenty Fourteen is fine. Just be aware that your change will be lost once you update the theme. But hopefully WP Fastest Cache will be fixed before then.

search console is currently having trouble because I changed the suffix from? amp = 1 to \ amp in time everything will return to normal, right? anyway thank you very much.

Yes, once Google Search re-indexes your site then your have AMP pages should show up again in search results like they were before. It seems like this can take several days.

Your AMP pages may also not be getting listed due to the validation errors.

in fact you are right. which plugin should i edit?

You should create a new one: https://developer.www.ads-software.com/plugins/plugin-basics/

This is better than editing a plugin because you won’t lose your changes when an update happens.

Actually, I also see that WP Fastest Cache Premium is causing another AMP validation error. In particular, it is adding this markup to the end of the page:

<noscript id="wpfc-google-fonts"><link crossorigin="anonymous" rel="stylesheet" id="twentyfourteen-lato-css" href="https://fonts.googleapis.com/css?display=swap&family=Lato%3A300%2C400%2C700%2C900%2C300italic%2C400italic%2C700italic&subset=latin%2Clatin-ext&display=fallback" media="all">
</noscript>
<script>document.addEventListener('DOMContentLoaded',function(){function wpfcgl(){var wgh=document.querySelector('noscript#wpfc-google-fonts').innerText, wgha=wgh.match(/<link[^\>]+>/gi);for(i=0;i<wgha.length;i++){var wrpr=document.createElement('div');wrpr.innerHTML=wgha[i];document.body.appendChild(wrpr.firstChild);}}wpfcgl();});</script>

You may able to turn off the that font optimization logic in the WP Fastest Cache plugin. It looks like there is a wpFastestCacheGoogleFonts option somewhere that can be configured in the UI.

Then again, you may want to consider switching to another caching plugin that we’ve determined is AMP-compatible. We’ve put together a list of plugins we’ve tested: https://amp-wp.org/documentation/getting-started/amp-site-setup/page-caching-with-amp-and-wordpress/

After a long constructive comparison with the premium assistance of Wp Fastest Cache, a PREMIUM version has been released which fixes the compatibility errors with the new features of the AMP plugin.

Now everything seems to be solved.

Thanks for the support.