Welcome to the Fusion 360 community!
Some of file formats are unitless. Depending on how you're bringing the data into Fusion 360 (Insert vs. Upload command) the scale will be determined automatically or you can set it yourself by choosing a unit. Either way, we just added a sketch scale command that should help correct any issues you have. You can check it out on the latest design differently blog post for the July 27th release.
I note that if you use the Insert DXF command (see the Insert drop down menu) AND the file is unitless, then you will get a warning and the option to modify the units will appear. At this point, you can choose mm or in or cm if you know what the originate file was designed in.

With regards to the second half of the question. The origin is absolute! You can use the Move command to move the sketch close to the origin, but there is no moving the origin.
I note that if you use the Insert command for DXF, you'll see the option to move the sketch in the workspace and place it before selecting okay.
I hope that helps! Let me know if you have any other questions.
Thanks,
Nathan Chandler
Principal Specialist