How to define DATUM H?

One more question... is a line enough to determine TP for other dimensions, or is it better to create a plane?

the snip you gave doesn't depict the size of those surfaces aside from about 0.150" of edge surface.    If you've got significant height and you sample along that height, your intersections will become a line, once you create a cylinder to intersect with. 

In the event those lines are non-parallel, you will increase your uncertainty in establishing that datum, unless you construct max inscribed planes or a max inscribed width somehow. 

-Or-

If your print defines a plane or known Z value to judge Datum H along, you can create a theoretical plane at that specified Z height and further refine your datum by intersecting your Planes-Cylinder intersect lines into that theo Z plane.... making them into two points again.

the snip you gave doesn't depict the size of those surfaces aside from about 0.150" of edge surface.    If you've got significant height and you sample along that height, your intersections will become a line, once you create a cylinder to intersect with. 

In the event those lines are non-parallel, you will increase your uncertainty in establishing that datum, unless you construct max inscribed planes or a max inscribed width somehow. 

-Or-

If your print defines a plane or known Z value to judge Datum H along, you can create a theoretical plane at that specified Z height and further refine your datum by intersecting your Planes-Cylinder intersect lines into that theo Z plane.... making them into two points again.

I know this is not enough information. This is the window on the side of the tube.
See the picture below, it's simple but that's all I can show.

Looks like your datum G can be a mid-plane made from 3+ points top and bottom, and your H can be a midline left and right. 
Either way your part is less than 1" so no matter what you do its gonna be a bit sketchy, you don't have much surface area to work with. 
I would not try to match the angle either, you will be picking up your points a bit off of the perpendicular vector, but also won't ever risk shanking out. 

Thank you!

Depending what's called to them or how the Demon is feeling today, you might have to take that data and turn it into different feature types to be valid datums.