I will say upfront that I do not have any knowledge of the Army ROTC program being as a member of the CG. That being said, I can offer a little AD military perspective.
Unfortunately, there is a stigma in the military that those on long term medical profiles, or "chits" as we call them in the CG, are not pulling their weight or "sandbagging" because they cannot fully participate in all activities. Why does it exist? Because, in the past, there have been cases where people stay on profiles in order to get out of activities. That is why your question number one is occurring - is it common? I couldn't answer that, it's well-known but it really depends on the command climate and leadership of others on how often the topic is broached.
3/4) I did a quick search and found a likely outdated but still potentially relevant Army instruction: AR 40-501 Standards of Medical Fitness
http://cdm16635.contentdm.oclc.org/cdm/ref/collection/p16635coll11/id/672
Chapter 7 (Page 73) is dedicated to profiling - both Temporary and Permanent Profiles
A temporary profile is given "if the condition is considered temporary, the correction or treatment of the condition is medically advisable, and correction usually will result in a higher physical capacity." I'm making a guess that your daughter is on a temporary profile, so the stipulations is that if your DD is on a profile for greater than 6 months for the same condition, she will be referred for further evaluation to determine a) continuation of the temp profile for up to 12 months, b) Change the temp to a permanent, c) Determination if she meets medical retention standards per Chapter 3. If the last happens, she could be referred to a Medical Review Board to determine if separation is necessary. Chapter 1 states that the U.S. Army Medical Center or Medical Department Activity are the review authorities for retention in all ROTC programs and appointment as commissioned officers from ROTC.
That's just come quick background information that I could come up with. What I would recommend is that your daughter engage with a officer POC at her Guard unit to assist, particularly if someone there has done ROTC in the past. They should have access to Army based documents that may be a little more updated. She should also continue to engage with her command at her ROTC unit about the issue and, if necessary, work her way to the next level (someone else on this forum may know what that level is). This is why the chain of command exists. If her cadre or the LTC are not giving her satisfactory explanations as you say, that is why the next level exists. To be honest, if your daughter has been evaluated by competent medical professionals (especially if they are Army medical personnel) and the police information proves injury, the cadre have to accept that medical information regardless of how they feel about it.
2) That being said, the cadre are within their authority to award an average grade of C or C- because she is unable to meet the requirements. It is no fault on her end but there is a standard and if it cannot be met, then an A grade can't be given. The reason likely shouldn't be that "there's no way to prove x" but rather that the "member is currently unable to fulfill all requirements due to outlying reasons and therefore cannot be fully evaluated." Your daughter was placed in an extremely terrible situation, there is no doubt about it. It is not something she should have had to experience and her command should support her. However, the ROTC unit (and her chain of command) also have an obligation to evaluate all of their candidates for commissions. If, because of the injury, your daughter is unable to get past the hurdles and become fully fit and capable of carrying out her duties, than the unit has obligation to act accordingly and potentially process for separation. I'm not saying that should be or will be the case, but it is a factor. The Army, and military in general, is a business. They are willing to patch you up and get you back out to work, but they can't be responsible for you if you cannot work at 100%, particularly if a commission hasn't happened yet. The 100% includes the PT portion. It's a hard truth but one that needs to be understood. I've been there and have the DD-214 to show for it. Fortunately, I was able to make it work, get healthy, and rejoin.
This is my two cents, it may not offer you much help other than a potential resource but I felt compelled to give it a shot. Good luck!