Well the healthcare question is relatively easy, if you spend that amount of time in California you don't qualify for Canadian healthcare anymore, and as you're self-employed you'd basically be paying out of your own pocket for it.
Your tax situation is going to be hideously complex I'm afraid because the new tax treaty requires proportional payment of
taxes based on where the work is performed and you clearly would have a "permanent establishment" in both countries.
US citizens have to file a 1040 return every year, regardless of where they live - if you already are one and you've never filed, you need to sort your situation out with the IRS before you do anything else, they usually require you to file for the last seven years unless they think you've intentionally evaded paying taxes (note there may be something in the indian treaty though that changes this, for example if you are treated as a US national rather than a US citizen - if you're a US national you don't have to file until you're in the US).
Anyway, once you're in the US you have a choice - file as resident in the US and non-resident in Canada, or vice versa. You pay less tax filing as resident in the US but on the other hand you might still qualify for healthcare in Canada if you file as resident there.
The paperwork you file varies based on your situation:
If you're a US citizen claiming residency in Canada, you file a 1040 in the US and state you are non-resident and file a T1 (as normal) in Canada and claim a foreign tax credit for income tax paid in the US.
If you're a US national claiming residency in Canada, you file a 1040NR in the US and file a T1 (as normal) in Canada and claim a foreign tax credit for income tax paid in the US.
If you're a US citizen claiming residency in the US, you file a 1040 in the US (like any other American) and file a non-resident T1 in Canada and claim a foreign tax credit in the US on Form 2555 for any income tax paid in Canada. (Note the maximum foreign tax credit you can claim in the US is based on an income of $85,700 for 2007 - over that amount there are some cost of living expenses you can additionally claim but they're minimal for Canadian residents).
You have to register as self-employed in both countries and do proportional payroll withholding based on where you were when the work was performed, which is going to get really messy, I don't envy you that task (in one country you would have to withhold as a non-resident, non-resident withholding rates are different, code 0 in Canada). You will also be paying CPP and social security - one minor advantage is that because your pay is split into two different halves it will reduce your contribution limits so your taxes might work out a bit lower than they would if you were in one country or the other all year.
You can still claim the full amount of social security you're entitled to when you retire under the totalization agreement.
As for your wife this is going to be a treaty question, you'd need to look into what the treaty actually says, she may be able to qualify for naturalization or LPR status if you put her down as a dependent, maybe not.
Steve.