User Manual Hamilton Beach 49979 Flexbrew Singleserve Coffee Maker Compatible

The coffeemaker brews up to 14 ounces at the touch of a button, then stops automatically.

That's hard to say since I do not know the standard dimensions of most travel mugs. There is 7 inches of clearance between the stand and the spout. If your cup can clear that, then it will fit your travel mug.

Cupcake liners are not a good idea. The paper is a different type, made to hold liquid, and won’t filter. You would have to perforate with many holes, with sketchy result.

Yes, you can brew all of the water through, or turn the unit upside down to drain all of the water out.