Will FM 19 open FM 10 files without us first having to save them into a different format?

As Jeff said, yes, you can simply open FrameMaker 10 files with FrameMaker 2019. You will get an "created with an older version" warning, but you can suppress the warning for subsequent files. If you want an automated conversion of folders (and optional subfolders) of the files from FrameMaker 10 to FrameMaker 2019, please take a look at my ConvertDocs script at www.frameexpert.com/store/

Not sure what you mean by "a different format", but yes, FM2019 will open and upgrade FM10 files to the FM2019 level, just like every other version of FM has ever done. Always make sure you've got a backup of the FM10 content because (just like every other change of version in FM's history) it's a one-way street. The only way you can go back is through a MIF save.