1) The google search results seem to have corrected themselves. I found the portfolio items are the bottom of the home page and hence not sure why Google would show them in the preview. If you have not already done so, I recommend you use an SEO plugin for your site to take control of this. I use WordPress SEO plugin by Yoast before and served me well so far
http://wordpress.org/plugins/wordpress-seo/
2) For the logo issue on mobile you can use the following custom CSS ( with logo size varying so much and with many device resolutions it’s hard to come up with something that works well in all situations) –
@media only screen and (max-width: 479px) {
#site-title a { background-size: 70%; }
}
3) Hard to say – depends on the kind of customization you have made. If it’s all just custom CSS, should be ok. If there are php code changes too, we need to be careful. Either way have a backup that you can revert back.
I would recommend you have a subfolder/subdomain where you have a fresh install of WordPress, load the latest version and reapply these changes you made. If you feel everything looks normal,just move the theme files back to the original server. You can try having a child theme to make these changes so that you do not have to repeat this for future updates. Hope this helps.