Hi there, it sounds like you’re asking questions about the WordPress.com version of Cubic. You’ve found yourself in the www.remarpro.com forums for self-hosted folks, who are running the WordPress software on their own hosting.
You can learn here about the differences between WordPress.com and self-hosted (www.remarpro.com) sites:
https://en.support.wordpress.com/com-vs-org/
I’ll answer your questions here for now, but if you need help with a WordPress.com site in the future, please go ahead and post over in the WordPress.com forums:
https://en.forums.wordpress.com/
1. Display pages on the homepage rather than posts
You can set a static page to be the front page in any WordPress theme.
2. Remove the date from the posts that display on the homepage (also remove dates from post headers)
You can do this with custom CSS, which on WordPress.com is a feature available with the Premium or Business plan.
3. Remove the menu items that display below the search bar
Do you mean the items in the “Recent Posts” area? That’s a widget, so if don’t add that widget then it won’t be displayed.
4. Customize the menu above the search bar (currently it’s defaulting to “Menu” as the title)
You can customize the menu by adding whatever elements you like. The word “Menu” is fixed, but will display in whatever language you set your site to.
The word “Menu” may also be hidden with custom CSS if you prefer.
5. Remove the “Create a free website or blog at WordPress.com. | The Cubic Theme.”
You may not remove the footer credit on WordPress.com – all users, including our VIP clients must keep the credit present to be hosted on WordPress.com. You may adjust its look and feel with custom CSS to match your other customizations as long as the credit remains legible.
On a self-hosted site (running the WordPress software on your own hosting) the credit is not required.
6. Remove comments from posts
Sure, you may turn off comments on pages or posts in any theme.
https://en.support.wordpress.com/enable-disable-comments-for-future-posts-pages/
https://en.support.wordpress.com/enable-and-disable-comments-for-published-posts-and-pages/
7. Integrate plugins
WordPress.com has dozens of plugins built in, but you may not add third-party ones; that can only be done on a self-hosted site, where you’re running the software yourself. If you let me know what kind of plugin you’re looking for, I can tell you whether WordPress.com already has it.
Let me know if you have any other questions.