This is a very broad complex issue which is difficult to answer with any hope of usefulness. I am/was father to my chronically ill, physically and mentally disabled daughter Nellie who died in the summer of 2005 shortly after she had turned 7. I am relatively certain that her care was as good as what we could have expected her to receive in the US, and that we didn't have to worry about going bankrupt due to the costs. But in terms of services (therapies, practical help at home, etc.), it depends an awful lot on where you are within Finland. We were in Turku until Nellie was almost 6, and Turku is well known amongst parents of disabled children for being a particularly bad place to be if you want decent services. We did receive quite a lot of help even in Turku, but we had to pretty constantly fight for it. We got therapies and a certain number of taxi rides per week to get her around, some home help for my wife every week so that she could get a breather, and money my wife received so that she could stay at home and care for Nellie. For many years, Turku paid my wife the middle class of that home care money, although my daughter required full-time care and technically speaking should have qualified for the highest class. Our opinion of course, and no use arguing at this point.
During the spring of 2004-2005, we wanted to get a lift system installed to help us handle Nellie, since she was getting very tall and heavy (even though she was disabled, I am very tall and Nellie got those genes from me). In Turku this was not going to be possible. So we moved a short distance outside Turku at that point to Lieto, and from a services perspective things improved quite a lot. We still got taxi rides to therapies, speech, physical, and occupational therapy, 12 hours of home assistance per week. My wife's home care income class was raised to the highest level. Most importantly, we felt that the system cared about our situation and really did their best within the existing system to help us. Nellie was about to go to a special school for disabled children when she suffered a stroke during the summer of 2004. At the school, the town of Lieto was going to provide her with a full-time assistant to help her through the school days.
It should be stressed that even though we did receive quite a lot of help, my wife had to work hard to get it. And there are always problems with any system. I am American and I alone couldn't have managed it. The administrators generally could speak English under duress, but it was never easy, and a translator was provided only once. My wife is Finnish and did most of that stuff. Dealing with the medical establishment is a whole 'nother can of beans. I have always imagined that American doctors are likely more sympathetic, at least on the surface, than most Finnish MDs. I have generally had a difficult time dealing with the Finnish MDs as I have found them to be overly professional when some humanity would have helped a great deal. There are always exceptions of course, and stereotypes shouldn't be made based on my experiences. And as I stated above, this may all be in my imagination since I've been in a foreign country for all of this.
The last year of her life, Nellie was in a respite care home. That was undoubtedly the worst year of my life. She was too sick to come home without full-time nursing care in our home, and neither Turku nor Lieto could find nursing care for us at home due to a nursing shortage. We weren't sure we wanted to bring her home with full-time nursing, and our uncertainty contributed to them not finding enough nurses. In this case we have definitely cried over spilt milk because we would have done things differently knowing how things were to end up.
To answer your exact questions: The amount of money a parent will get DOES depend on the "severity" of a child's illness, but the amount will not be nearly what a parent would make at work. Not even close. But it is SOMETHING. The parents of a child who can function, i.e. feed him/herself will receive somewhat less than the parents of a child who needs full-time care, i.e. to be fed, clothed, etc.. There are usually 2-3 classes in my experience, but I am not an expert. My wife received around 400-500€ / month (difficult to remember right now).
I hope this helps. I am glad we were here in Finland for Nellie's life. We had no idea she'd be disabled when we moved here (my wife was pregnant when we came), but I have always been relieved that we were here rather than in the insurance-driven American medical system. Just my experiences.
Wishing you all the best,
Peter Lingenfelter
peter.lingenfelter@gmail.com