SingeFile saves the HTML and, if you enable it, some JavaScript as well.
The images are saved INSIDE the document. This trick is performed by taking the image and encoding it into a super long string of characters: base64 encoding. You can try this out for yourself: https://varvy.com/tools/base64/
This is what makes these files so large sometimes
You can verify/test what/how SingleFile saves a page by saving a copy, then disconnecting from the internet and loading the saved page.
Yes, you can save the embedded images: they behave the same way regular images do.
If you want to save a page including assests, and would want animated GIFs to stay animated, a better option is to save the page the normal way with your browser, opting for Save Complete Page.
If you prefer the 1 file format you can also save as MHTML. Chrome can show these as well but to save as MHTML you need a plugin like save as HTML
An MHTML file is essentially a ZIP file. It contains the HTML page and all the files linked in it.
Archive.org works the same way Google does: it crawls a website and saves a local copy of the page, uncompressed.
Scrapbook for Firefox is a similar extension but with a bit of database/search-like functionality added.
The Tagspaces Chrome extension does MHTML saving. It’s a companion for Tagspaces but works without it too.
Besides saving text of pages to Evernote or grabbing content otherwise (like with wget), SingleFile is the tool for me to capture a page as close to as it is.
Happy you like it!