No. Asking is the key, though. I hate it when I'm walking somewhere, and someone just grabs my arm without even asking. Similarly, when I'm working in the kitchen, and someone just starts helping, without saying anything. I probably had what I was doing all planned out, and now you've moved stuff so I can't find it, or gotten me off schedule, or whatever. If someone asks, sometimes I'll want help, and sometimes I won't. As long as you take "no" as a valid answer, then it's not offensive. Sometimes I want to do things myself, even if it's harder for me and I'm slower at it, because I want the practice, or I just enjoy doing it. Other times, though, I'm in a hurry, or it's something I already know how to do but hate doing, and would be glad of help.

I would just ask. Something along the lines of "hey it's clear that you're really independent but if you're ever in a pinch and need a hand with something just let me know".

The best way to go about offering help is to introduce yourself (don't assume people will recognize your voice. Even with coworkers I've worked with for years, it can be tricky to recognize voices), then offer them assistance. If they don't need any, they are free to turn it down.

Some people get super sensitive about it, but it's fairly rare.

Not offended, but annoyed. I don't get out of my comfort zone so I don't need any help, and the people who provide help are denying me experiences that I should have on my own because they won't be there to assist me all the time. If I need help I'll ask for it, but before that I prefer to try and fail.

Maybe offer something if specific to help with. Grass mowing, a ride to the store, etc.

No just make sure you don't treat her in the "childish you can't do anything" way. I love when people offer me help because, even though I'm partially visioned, I still need help.
The best way to say it is to ask if they ever need anything you're there to help. Just don't suggest because they are blind they can't do anything.

I don't see (heh) a problem with it. Don't just try and do it for me (example, when I'm standing in the elevator and ask you what floor, don't just reach over and hit the button for me...that kinda irks me a bit), but I certainly don't mind if you just say something like "Hey man, need some help?"

At least with me, just make it casual. Like if you saw someone holding or carrying a heavy box, just a friendly offer for help. Even if I'm just fine doing whatever I'm doing, the thought is definitely appreciated.