-
The pull travels along the string at the speed of sound. You've asked us to assume, hypothetically, that sound travels at infinite speed in this string. That is not allowed in relativity.
-
I guess you want us to treat it as a really long particle, so yes, I think it would. However, nothing like this will ever be done, and even if you get close, it won't be instantaneous.
-
The impulse would travel along the string at the speed of sound which won't be faster than the speed of light. So at best it will ring a year later.
-
a bell is never instantly rung when you pull the string because the movement of the sring takes time to cause an affect but it in this case it would take longer :)
-
A time delay, but you wouldn't know because there's no air in space to transmit the sound, and it's too far away anyhow.
-
If the string has no elasticity, then you won't be able to tug it will you? It will in fact be a straight bar.