What are files with "mui" extension?

According to Bing, the Mui file is a language file that allows IE to run in english, spanish, chinese, etc.

So there should be some of those but I don't think they should be the main file.

Concerned what full filename is supposed to be.  Is filename sapisvr.exe.mui correct (with embedded "exe"). True filename or potential virus?

That's perfectly normal - there is always also a file with the bare  extension (usually in the folder above the one with the .mui file)

If you look in the C:\Windows\System32\en-US folder (assuming your language is English) you'll see over a thousand .xxx.mui files - all have matching files in the C:\Windows\System32 folder.

If you're in doubt about ANY file, you can upload it to www.virustotal.com for a concerted opinion from over 40 Anti-Viruses.

.mui files are no more or no less likely to be infected with malware than any other file extension. A file extension in and of itself is not predicative of malware. Rather the source of the file is the culprit. Downloading files from trusted sites, as well as maintaining anti-malware software is key in keeping a healthy PC.

Incorrect - if you have a .mui file in that location, it's quite possibly malware!