1)I have loaded 2.0.14 CB and 4.0 CB Subs. Several issues. Finally figured out how to get both the Contact Info and Membership (subscription) to show as tabs and the Edit to appear on User Profile (menu) but the edit button does not work. There is a connections as well and nothing happens when I click on that. What is it anyway and how can I remove it?

If they're not working then you probably have a JS error breaking their JS. Press F12 to open the browser developer console. Next click the Console tab and refresh the page. If you see any red JS errors on refresh or after clicking then you've a conflict. First ensure you've latest nightlies installed though.

CB 2.x Nightly:
www.joomlapolis.com/downloads/doc_details/640-community-builder-nightly-build

CBSubs 4.x Nightly:
www.joomlapolis.com/downloads/doc_details/671-cbsubs-gpl-nightly-build

2) When I logout it takes me to login page. How can I redirect to home page instead?

Within your CB Login module set the logout redirect to index.php (should be default set to this unless changed).

3) When I login again it takes me to a "Profile" page? Different from the userprofile page? Why is that, where is that and how do I get it to just take me to the home page when someone logs in?

There's no login redirect specified by default. Sounds like you are not using CBs Login module, but are using Joomlas. Please read your CB 2.0 Primer Book carefully for install and configuration instructions or see the below videos.

www.youtube.com/playlist?list=PLp0puRITgC7PuyzPsMUECDI46VE7IFSAX

4) If there is a photo added, it covers the Edit so you can't see what to do?

Looks like you may have disabled the canvas field, which defeats the purpose of the canvas layout. You'll need to use the canvas field or adjust your tab position usages to accommodate for it not being used.

#2 and #3 Logoin/out redirect - I am using the CB Login. Logout is set to index.php When I logout it takes me to where I can logon again. I want to go back to the home page.

You should be sent to your home page if your logout redirect is set to index.php. You need to ensure you're using CBs login module to logout or CBs logout Joomla menu item though. If you're using Joomlas I've no idea where it's going to send you.

When I login it takes me to a profile page. Should stay on the page where I login?

By default CB does not send you to profile on login. You would of had to configure that within your CB login module. Within Extensions > Modules filter "Type" to "CB Login" and review the configuration of each module carefully.