I live in Central LA (near LACMA / La Brea Tar Pits), and share my neighborhood with dozens of homeless. Most of the homeless in my area are what I would deem "regulars", as they tend to sleep / hang out in the same spots day in and day out. I can't tell you how they landed in the situation they are in, but I can safely say that 9/10 appear (and I'm not a doctor, so I can't obviously say for certain) to have at minim…
Moreover, why does treatment have to come at the expense of self-determination? The reality is that people want to receive treatment--if they don't, it is because they encounter a barrier to treatment.
Barriers to treatment include: lack of treatment facilities (hospitals do not count), poor quality of existing treatment facilities, unwillingness of treatment facilities to take anything but an abstinence-only approach, lack of other treatment options, such as medically assisted treatment.
So I would say yes to all your points, except number 2. If people don't want to recieve treatment, then we should assume that the treatment isn't good enough and needs to be improved. But indefinitely detaining someone in a place that they don't want to be is frankly a human rights abuse, and contradicts your first point.