1/ In edit each page screen, scroll down and you will see option for hide page title.
If you want to hide all page titles, please add more this code to Customize > Custom CSS:
.penci-page-header{ display: none; }
2/ To do that, please go to Customize > Logo and Header Options > on “Header Layout” > select “Header 4” or “Header 5”
3/ Seem you did add page “Home” to your menu.
Please go to Appearance > Menus > remove page “Home”, after that use “Custom Link” on the left side > Copy and paste your site url to “URL” of Custom Link ( include: http:// or https:// ) and add it again to your menu, replace with old “Home” menu item.
4/ Please make sure you’re using latest version of Portfolio. If not, go to admin page > Plugins > delete Penci Portfolio plugin > go to Appearance > Install Plugins > re-install “Penci Portfolio” plugin.
After that, check shortcode for Portfolio here – use parameter “number” to set number portfolios display on each page.
5/ This theme supports 4 socials sharing: Facebook, Google+, Twitter and Pinterest. And this theme doesn’t support select/change that social icons for posts.
By default when you click on the logo, your site will redirect to homepage. Have you edit the header.php file of this theme? If right, please update this theme to latest version and this issue will gone. Check this guide to know how to update this theme to latest version.