How does interest rate impact callable bond?

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?

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

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

I see., thanks!!