Modify Wordpress Site and Explain HOW you do it

Fix some pesky problems with WordPress site. Explain to me how you fixed these things. If you do well, this could start an ongoing relationship where I pay you to help me with various problems like this. Good English communication is a MUST. Ability to talk by phone or Skype required. Here are the problems I need fixed ASAP: 1. My logo has disappeared from the upper left of the site—to the left of the menu. The logo is [login to view URL] It needs to be a link that clicks back to the home page https://www.gmsa.org. 2. Protected content is not working right. We want a single username and password that can Sign in. All the members of our organization share this so they can access private info like a personnel directory, birthday calendar, and other internal information. The username is XXXX and the password is "XXX" without the quotes. When that user logs in, they are directed to [login to view URL] That is wrong. Instead, they should be directed to [login to view URL] It appears to me that the idea of a "website front end user" and a "Wordpress user" are not properly split. Also, the /calendar/ url is not private, but it should be. I would like to be educated as to how to make new private content. 3. Related to #2: Two menu-system that is set up in Appearance | Menus is clumsy. I don't want to have to manually update both menus when I'm updating part of the menu that is not protected content. Example: I added many "team members" under the "Team" menu in Menu 1, but it appears that I have to do all that work again under Menu 2. This doesn't seem right. 4. On page like /overview/, I would like a gallery slideshow without a huge black space around it—just the picture, rotating. I do NOT want to install some huge gallery manager. My prior website designer had used NextGen Gallery, but it seemed like it was slowing my site down a LOT, so I removed it. Is there a way to use the built-in Wordpress gallery to do what I want? 5. Add "Sign out" item to Members menu when the user is logged in. 6. Explain to me briefly the "theory" or "idea" behind Wordpress. I am fairly technical. A long time ago, I had a collection of php files implement this website. Then I converted it to CMS Made Simple so I could have page templates using Smarty template engine. Now a freelancer developer brought me fully into WordPress but every page is using some custom html, so I will have a hard time changing the site look and feel. It seems I have taken a step backwards. Basically all the pages have a lot of custom html and php on them in the "Text" tab. When you look at things in the "Visual" tab, not everything appears.