There is a valid question in there at the end that is not off topic,
[does] using just one image for several logos and icons...impact the accesibility of the website
Whether you have individual images and multiple HTTP requests or just one sprite image has zero affect on accessibility.
How you use the image (whether one or multiple) is what affects accessiblity.
Images that are used in the background (CSS
background:url(foo.jpg) with offsets) are invisible to screen readers, which is a good thing if the image is decorative.
If a background image is informative and has meaning, then that meaning will need to be conveyed to all users. That's normally done with the
alt attribute on the
<img> tag but if the image is in the background, then the image's information would have to be on the containing html element (or one of its ancestors).
But this is starting to get into implementation and would need to be addressed on stackoverflow.com. You can post there and use the
accessibility tag like you did on this question.
The simple answer to the gleaned question is 'no'.