There are almost no English-language facilities for special needs children in Finland.
In general, special needs children are accommodated in mainstream schooling, as far as possible.
Tähtiniitty koulu (Olari, Espoo) and Postipuu Koulu (near Leppävaara, Espoo) both have special needs facilities (physically and mentally handicapped children) and both are bilingual (Finnish/English) schools so I suggest you start there. However, AFAIK the special needs sections operate only in Finnish.
Children with less severe problems (eg ADHD, dyslexia, maybe Aspergers) generally go to the regular schools but sometimes an extra budget is given for a teaching assistant in the classroom. One of my kids had a friend with quite severe ADHD in his class (in a bilingual school), with a full-time dedicated teaching assistant... but a year ago the parents (both native English speakers) decided they really had no choice but to leave Finland.
There is also a special school in Kivenlahti, Espoo which helps children with more severe learning difficulties that cannot be accommodated in mainstream schools but IIRC it is all in Finnish. But I don't know much about it.
My advice would be to think hard before you come here. Finland is as cash strapped as everywhere else right now (despite its AAA rating) and quite drastic cutbacks are being made in education. I'm not sure that providing English-language resources to temporary residents is top of the list of priorities (it's the municipalities who have the budgets and make the allocations). Sounds hard but I guess you need to know what to expect.
Yes, special needs children do qualify for transportation (conditions apply) but in some cases some children are not able to use the special transportation (eg if they pose a safety risk to other passengers). So "It depends" is the answer to your question.
I'm sure there are activities for special needs children but they would be in Finnish.
One of my children has (relatively mild) dyslexia and ADHD and merely getting a thorough assessment for him here (in English) was almost impossible. In the end we flew in an educational psychologist to Helsinki from the UK and shared the cost with two other families... for example.
http://www.espoo.fi/fi-FI/Paivahoito_ja ... puu_School
(the headmistress (rehtori, in Finnish) can probably give you some advice on your best options, at least in Espoo. Call the school directly, all the staff speak English)