FAT32 is a filesystem developed by Microsoft, but hasn't been used for Windows installations for almost a quarter of a century. Although it has its imitations, fat32 is useful for such things as SD cards, USB pendrives, and - as has already been explained - EFI partitions. Heck - even Apple has been using fat32 for its EFI partitions on its Mac computers for donkeys years, and it would be misguided to think that the EFI partition on an Apple Mac is a "trace of Windows". As it would be just as misguided to think of all the USB pendrives and SD cards as having a "trace of Windows"
I re-iterate: do not delete your EFI partition. If you do, you will have a severe emotional reaction when next you try to boot your machine.
That's normal - nothing to do with dual booting. The advanced options choice is - well - advanced options for Ubuntu. The hint is in the text. You'll find the opportunity there to boot with the previous kernel and a memtest - at least last time I looked.
Without more information on his system, I doubt anyone could do more than guess.
One last comment: the output of the ls command in an earlier post of yours showed only BOOT and ubuntu folders, not the Microsoft folder than yancek thought might have survived. I hate to disappoint you, but even there, there is no trace of Windows that I can see.
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