Yes.
Does it annoy you when someone ignores your text messages or replies really late to them?
Very much. It also annoys me when your texting someone, than you have to wait 40 minutes and all they send back is 'K'. Thats so annoying!
Only if you were already having a conversation just then.
While since I am the person that you have described... Not really, if I do that its for a reason, and the person should think about the atmosphere, that being said if they're just rude then you can be irritated, however if you're me, that response is nothing except for rational.
It depends like if they had to do something extremely important then its okay
So much, I may actually confront them in person. But mainly if it says they read my message and didn't reply. I understand when people don't have the time to or even lost power in their electronics. But I feel like those are all the excuses.