Okay.
1: The Hayabusa are sensible by various amount of things with various factors. As you stated earlier, base senses may be able to pick up on a Hayabusa's presence. These include, however not limited to (in my eyes at this time): the 5 basic senses. Those being sight, touch, sound, smell and taste. Some abilities, clans, etc. that may be able to sense a Hayabusa normally would be the Inuzuka clan with their heightened smell, Ganmi in the sense of taste as they wouldn't necessarily need to lick you but taste something in the air around you to let them know you are there, even though anyone can hear anything unless they are deaf, besides hearing our footsteps like normal, an adequate sound user may be able to hear you from afar. These are the ways I perceive us being sensed. As you said, extrasensory perception will not quite work on us but the physical traits of the five senses will. We can also be seen obviously. So unless you are blind.... You know.
2: You can sense it is missing but you would not be able to tell where. You can sense if it went higher in altitude or lower in depth, but you could not pin point this. You could also tell that your arm is on or rubbing against something in the dimension, but couldn't tell what. You could locate it, but not be able to tell its altitude. Would I know it is Kaguya's dimension? No. If I had means of getting there would I be able to find it? Yes. No matter where it would be, you would only be able to tell where it is once you actually get there.
3: This is a cloudy area. Should you have mentioned another clan or technique I might be able to say spot on how the two interact with each other, however, this is tricky in my opinion. However, I think Yamanaka clan techniques would indeed work on us, however it would not take effect until a turn later, giving us time to disrupt and botch the technique/setup.
4: No. Chakra sensory on my Hayabusa has little to do with me being able to sense another Hayabusa. Firstly: that is considered extrasensory I believe and Hayabusa cannot be sensed by that. However as a Hayabusa myself I can sense all Hayabusa my rank and lower, but none above my rank unless they chose to reveal that to me. I think.
I think these answers are sufficient. Thoughts?