So he won't get therapy in school?
Grants for autism for therapy? Grants for single moms?
I saw the have Government housing. Is this easy to get?
Can I file and receive taxes each here like in the US?
He will be likely out of school once the immigration process is completed.
There is no special "grants for autism therapy for adults". There may be grants for single parents but if you qualify to immigrate under the economic stream, you are unlikely to qualify for those grants/social assistance.
Government housing take decades (10s of years) to qualify. So many people are in housing crisis.
If you become an US citizen, you will need to file your US tax. And if you immigrate to Canada and become a tax resident, you will need to file your tax return with CRA as well.
There is treaty between the 2 countries and you won't be double taxed.
Just a note. Unlike what a lot of people thinks, healthcare in Canada is NOT totally free.
Healthcare coverage is provincial (different in each province) and while visiting a doctor and hospital is free, medication/drugs, other therapy and treatments are NOT free.
Equipment and many services are also not free. Dental visits are not free (at least for now for most adults)
Some of those costs are covered by employer's extended health coverage for their employees. But if you are not looking to be employed, you will need to pay those out of pocket.
There are also co-pay and limits on coverage by those extended health coverage. (e.g. I only get $500 a year for physio and I have to pay out of pocket once the 5 or so visits are done. It can easily go over.)