I don't believe you can just change capacitor value. Grid resistor value will need to be changed to maintain time constant for the stage.
Correct. People do only one or the other all the time to either accommodate a less hardy output, or to add an extra bottom octave to the frequency response that the original designer somehow forgot. And make a mess.
The K40 in the top picture is physically much smaller than the ones I've used there. Then again, I tend to use ones that are one to two voltage ratings higher than original spec; 630v and 1kv. Never had a problem with these little Soviet cans, ever.