Ideally yes. The only reason to use the H1 tag twice would be for screenreaders.

However, I'm fairly certain you will not see a change in rankings if you choose to repeat your H1 text twice on one page.

Hmm. Try making a video sitemap with a few videos that currently aren't appearing in serps, submit to GWT and see if they appear in a week.

Is the quantity correct?

You just need to do some detective work in GA and see when/where the product purchases were logged. How many different people? Did they revisit the same page (as you mentioned)? Where is your conversion tracking code located?

There are so many questions/possibilities that it's hard to determine without actually going into GA, following the conversion funnel, troubleshooting on page analytics code and analyzing the situation.

amazon, zappos, walmart, microsoft store - many ecommerce sites don't use tabs.

A common workaround seems to be to have "tabbed navigation" but instead of toggling visibility, it scrolls down to the corresponding section.

Looks like you are doing everything right (set up 301 redirects, updated all links on the site, updated canonical urls) - just need to force the crawlers to parse those pages more. perhaps crawler is hitting its budget before it gets to recrawl all of your new urls?

You should also update your sitemap as it contains a bunch of links that look like: https://www.gomme-auto.it:443/pneumatici/estivi/pirelli/cinturato-p1-verde/145/65/15/h/72

I recommend creating several sitemaps for different sections of the site and seeing how they are indexed via GWT.

When did you set up the /folder/ property? I've used this to get more detailed backlink reports (as the "links to site report" is different when you enter a subfolder). What data are you looking to get?