I was not really wanting to spell this out as I don't want to come across as crass and insensitive, but here are the issues with these point:
• If a student has given consent for the parents to be informed about their mental health problems and they know the student is suicidal, inform the parents.
The problem here is a potential man-slaughter charge. A student tells their tutor they feel suicidal. The tutor is unable to reach a parent (it would be totally inappropriate to leave a message on an answer phone) tutor then has other work to do and then is whizzing out of the door forgetting they haven't made contact with a parent. Student takes their own life and now we have a tutor who is potentially indirectly responsible, and could legally face a man-slaughter charge.
You would also need a signed document from the student saying it's okay to inform parents, otherwise the tutor could face disciplinary charges for breaking confidentiality, then the signed doc might be null and void because the student could argue they weren't compos mentis at the time, so now a tutor has to know the laws around capacity and would need to fill out a capacity assessment.
Then there is note keeping, where does the tutor record they've tried to contact the parent. Etc etc. as I previously mentioned it's not straightforward.
• if the University is aware a student is having a severe mental health crisis then do not continue with the process of dismissing them from the University - by email - without consideration. I can't answer for all universities, but having been a uni student a few times, being 'sent-down' only happens in extremis, but if someone is not engaging what are the uni meant to do, how else do they reach the student if they are not attending classes or answering emails / haven't requested a deferral etc? I'm fully aware that spiralling mental health means engaging with tutors / lectures / pastoral care even health care professionals can be nigh on impossible, it's a very tricky situation and there isn't an easy answer to this.
• If a student has visited support services with a mental health issue that has not been resolved, do not tell them they cannot have a follow up appointment with Uni support services until the next academic year.
If support services haven't managed to help resolve the issue, then it would be potentially unethical to keep offering a service that isn't working. I don't know if the university support services are run by actual qualified healthcare professionals, if so they should be able to refer on to NHS services. If they are more a support team without clinical training, then there are problems with record keeping and confidentiality.
Yes better funding is needed. Having out reach mental health teams visiting universities on a weekly basis could be a way forward. But you can't put the onus on lecturers/ tutors or pastoral care to support illnesses. I wouldn't expect a tutor to give me crutches for my broken leg, because it's not their remit.
Mental health is very complicated, it needs more research, it needs de-stigmatising, it needs a ton of money poured into. We all need much better understanding, but putting the onus on universities is not the answer. Blaming parent is abhorrent. This is an illness, it's no one's fault.