Yes, TimeFrame = AssetFrame is sufficient.

JCL,

I discovered that TimeFrame=AssetFrame works only in whole hours. E.g.:

will end the Daily bar at 17:00 ET.
But with FrameOffset=50 (i.e. 1 bar less), the daily bar will end at 16:00 ET, not 16:40.

Can this be behaviour be changed to the expected?

Also, can AssetZone and TimeFrame be called in a function?

Yes, as I understand the manual, AssetZone sets the time zone for hour bars. So for individual offsets and different bars you need to set up TimeFrame individually. You can use a function for that.