Oh dear, so much for the best laid plans etc. There I was, 10 days ago, about to write an answer the question 1 of my latest Five Questions when the dreaded gastric flu lurgy struck. Still hopefully I’m OK now, back in the land of the (semi-)sane, and we can resume what passes for normal service.
So to our question …

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Question 1: Does killing time damage eternity?
Crumbs, you do ask some difficult ones don’t you!
First of all we need to understand what time is and what eternity is. And we don’t. No-one has yet agreed. Even our top physicists really don’t have much of a clue what time is. See for instance physicist Sean Carroll and Wikipedia.
And if we don’t understand time, we cannot understand eternity. For eternity is just the infinite extension of time. And how to understand the infinity of something we don’t understand.
But there, we now have a connection between time and eternity. So anything which affects one of them can logically have an effect on the other. But what effect? We don’t know, because we understand neither time nor eternity.
But then again we have the wisdom of Terry Pratchett in Thief of Time …

Wen considered the nature of time and understood that the universe is, instant by instant, re-created anew. Therefore, he understood, there is, in truth, no Past, only a memory of the Past. Blink your eyes, and the world you see next did not exist when you closed them. Therefore, he said, the only appropriate state of the mind is surprise. The only appropriate state of the heart is joy. The sky you see now, you have never seen before. The perfect moment is now. Be glad of it.

And …

Time was something that largely happened to other people; he viewed it in the same way that people on the shore viewed the sea. It was big and it was out there, and sometimes it was an invigorating thing to dip a toe into, but you couldn’t live in it all the time. Besides, it always made his skin wrinkle.