I was under impression Linux uses the term swap partition (or swap file if it's in a file which is much less common) while Windows calls them either swap files or paging files. Looks like you're right and Windows uses these terms interchangeably.
Just for the sake of correctness: phones almost definitely do have virtual memory, that's how any modern memory allocation works. You probably meant swap files/partitions.
Sadly yes. It's especially evident to me whenever LineageOS is mentioned as THE way to install a non-standard OS. Not that long ago there were dozens of options for each device and Cyanogenmod (the grandpa of LineageOS) was just one of them, albeit a quite large one.