Nursing manners (which for me includes all interactions with my boobs) have been a constant, low-level issue for us. I find that it's really best for me and my 2 year old nursling when I'm 100% consistent and firm about what is and isn't permitted. It cannot be "some of the time", that just makes everyone confused and frustrated, and encourages her to keep testing the boundary.
1) No rummaging in my shirt without me. Ever. 90% of the time I will nurse when she asks, but mommy does all of the rearranging of the shirt and bra, and then I invite my toddler to latch. This was big for me from the start, because I found myself resenting it at 8 months old when she would crawl over and push right up into my shirt without even connecting to me. A mommy who feels resentful is just as much of a problem as an angry baby, so we found the boundary that helped me to feel respected, too. I needed some eye contact. She used sign and verbal cues to express hunger, and I always validated her asking, even when my response was "I understand that you want to nurse, we can nurse when I'm done cooking, would you like a cup of water now?" If this sounds good for you, it might help to wear sweaters or high-necked fitted shirts for a few days to help you draw the line. This has not been much of an issue for us, I think because it was easy to be consistent about from a very young age.
2) For biting, scratching, twiddling the other nipple, kicking, all of those... I tried grabbing and redirecting the offending limb but eventually learned that the redirection needs to be processed through my toddler's brain and the only way to get her attention is to unlatch her. The first many times I unlatched her in response to mole-picking, or digging her toes into my belly-button, I got an outraged roar but quickly she learned that all I need is for her to look at me, hear me say "no mole-picking!" and I will immediately offer to relatch. Now the redirection is accomplished in 3 seconds, with little fuss, no wrestling, and good effect.
Realistically, she's an active and curious toddler and taking the time out to be attached to the breast is hard for her. So I try to accommodate this by having a small toy or a "nursing necklace" when I can (this is miraculously helpful) and by allowing her certain kinds of fidgeting, basically whatever she wants that doesn't hurt me or involve picking moles or nipples.
For us, the hardest hurdle has been the mole-picking, because sometimes she just wants to touch my cleavage mole and when she does it that way, I don't notice it. With my nipple, it's easy for me to be black and white - no touching! I think it's harder for her to understand the grey line between touching my moles gently and twiddling them in a way that makes me fear I'll bleed. I, too have thought of putting bandaids over them or getting a dermatologist to cut them off to simply put an end to the fiddling.
I hope my experiences can help you. For me, the issues that I've been able to be most consistent about are the ones my nursling respects most easily. When I need to institute a new boundary (such as no pushing on my now-pregnant belly) there is a week or two of outrage, but I try to talk it out patiently and immediately offer a "good" alternative such as a nursing necklace or something else to mess with.