Verma

Twenty Fifteen shows full article.If you want to show post excerpts then you need to make few changes. You may read this article for changes in code . Post excerpt in Twenty fifteen

If you just want to shift the existing sidebar to right side then you can easily do that. There are few CSS properties which need to be amended. You can look for details here Right sidebar in Twenty Fifteen

Your websites are quite slow.Sometimes poor connection also creates problem in plugin installation. You may try manual installation.But improve performance of your site.
Your server response in not bad but large number of http requests delay complete page load.
I think issue may be due to connection only.

There are several public host where you can host easily at quite a low price. If you host of your home, then bill for your home broadband will be higher and higher.I will suggest to host outside.
But as a technical solution, you can host website from home.Get a static IP address, install a web server in your computer , purchase a domain name and redirect it to your IP.

Yes you can add 728×90 ad in header but the ad will not be properly displayed in smaller screens.The basic property of theme i.e responsive behaviour will not be supported by your 728×90.
Google has already provided responsive ads which adjust according to width. You better place that code in header.

You need to enter ads in loop. Look at the content.php and other similar files for inserting ad code.
Remember that adsense do not allow more than 3 ads in single page.

Edit your post which you want to show as favorate. Set Visibility of post as : Public and select the checkbox ” Stick this post to the front page”. Set any image as featured image for the post to see image also in featured post area.

Until you pass details of changes you made,it will be difficult to figure out.

Why don’t you use non transparent header image with background as site background.You are using some plugins also so how they are affecting,I can’t say.

Create a child theme , that will save your site from several possible dangers. Then you can comfortably change the css properties of site.I guess that you are using twentytwelve theme so thing are pretty simple for changing background.
1. Create child theme.

2. This is the site background css setting in style.css

.site {
padding: 0 24px;
padding: 0 1.714285714rem;
background-color: #fff;
}
You can change site background from this css.

It is clear that function twentyeleven_content_nav() is not accessible.Look at the functions.php file. There you will find some clue. Function.php in child theme works in parallel to function.php in parent theme.So Check this function belong to which theme parent or child then locate the function and check for errors.