How does interest rate impact callable bond?

CFA Level II
#1

If interest rate goes up, the value of noncallable bond goes down; the value of callable bond goes down; the value of the call option is inconclusive.

Am I correct?

#2

interest rate go up bond value goes down so call option goes down because there is no point in calling a bond that falls in value and if IR goes down value of bond goes up and its likely to be called so call options value goes up

#3

The value of the option should go down too since it would far from the excercise price

#4

I see., thanks!!