1) Because, for better or worse, many professors see it as "academic inbreeding" to stay in the same lab for undergrad and grad school. In cases where people didn't apply to many schools, it could also a proxy of how serious the student is, whether they are applying to places that are best for them, or applying to places that are "comfortable" or "someplace nice" Of course, this isn't even on the "problem" radar for some folks, whereas others see it as a huge deal - there is a great deal of variability. I wouldn't fret over it too much though, what's done is done and as long as you have a good explanation for why your undergrad provided opportunities that weren't available elsewhere, its incredibly far down the list of things that will get you accepted or not (at least at other schools, I assume if the professor at your undergrad feels this way it would cause problems!), even for professors who do think applying to your undergrad is a bad idea.
2) Obviously depends on the prof. Overall, I would hazard a guess that they are looking for you to take responsibility for your actions. In other words, an applicant who responds "Because the professor was a jerk" likely kills his chances, whereas one who says something like "It was a really hard topic for me, and my grade may not show it but I feel I learned a great deal from the class, and have since gone on to do x and y related to the class and excelled at it" would get a gold star.
3) Depends entirely on the person. Don't lie because you don't necessarily know what your LOR writers said, and contradicting them would raise eyebrows. Of course, that can happen anyways since they may view your weaknesses differently from you, but I think its more likely to happen if you lie. I think the most important thing isn't what weakness you choose, but how you frame it. Someone who says "I'm a terrible writer. I mean really, really bad. My writing is completely incomprehensible, you can't even understand my emails, let alone a paper. Sometimes people think English is my second or third language, but its not. I mean, I know what I mean, right? If other people don't understand, that's their problem." is in trouble, whereas "I've struggled with writing throughout college because I sometimes have troubles organizing my thoughts in a way that makes them clear to others. I took a writing class and signed up for some writing workshops to help overcome this. Its an ongoing process, but I think my writing has come along way and I'm hoping I can continue to improve as a graduate student" is in good shape.
Obviously, extreme examples, but I think they illustrate my point. Its not the topic so much as the explanation that I think faculty look for.
Though of course, I still wouldn't say "I have no people skills" or "Numbers scare me" or something like that when applying to a clinical program😉