What does it mean Keep on Tender Hooks?

Answer 1

The phrase on tenterhooks means in a condition of (anxious) suspense.

For its origins and development, here is a paraphrase of the information as laid out in the on line OED:

A tenteris a wooden framework on which cloth is stretched after being milled, so that it may set or dry evenly and without shrinking. Thus a tenterhookis a form of hook (sometimes a bent nail), a number of which are set in a close row along the upper and lower bar of a tenter, by which the edges of the cloth are firmly held. The metaphorical use of the tenterhook means something that is stretched or strained; and by extension something that causes suffering or painful suspense.

The word was used in various phrases, such as to put, set, strain, stretch on the tenterhooks: to strain, distort the sense of (words); to strain (conscience, truth, authority, credit, etc.) beyond the proper, normal, or natural extent, limit, or scope; to put a strain on (a faculty, power, or capacity). None of these are commonly found in modern use.