Cover it with a thick lid.
keep it in a hot place
No. Use Styrofoam.
No, a galss cup does not keep any drink warm long.
warm it up every time it gets cold
You can keep it warm by keeping it out in the sun. If there is no sun, than I don't know how it will it will stay warm.
Yes it will .
try covering the glass, so the heat particles stay inside the cup, and the hot water stays hot.
Sit on it(incubate) /place int in hot water.
A plastic cup will not keep hot water warm for a significant amount of time. It is not an effective insulator and heat will dissipate quickly. It is recommended to use a thermal mug or a container specifically designed to keep beverages warm for longer periods.
It would depend on the temperate of the room, the amount of water, the temperate of the hot water and the thickness of the glass. (Also on the humidity, the elevation) So it's really impossible to say. I assume you mean a typical 250 ml glass, and the air was room temperate, normal pressure, humidity, fairly typical elevation... But, I'm still not sure what temperate of water you mean, which is one of the most important factors. 30 minutes perhaps?
The moisture in the warm air collects on the cold glass. When enough moisture collects, it forms beads of water that run down the side of the glass.
It would make a warm inked water! (I think this may not be true)