1) Taking care of a family member with cancer CAN be enough. But facts are key. If its is your 7th cousin with isolated skin cancer who is expected to survive? Not likely. Your parent who needs 24/7 care? Likely.
So you want to present the case to show severity and closeness. A statement from the doctor that lists why your help is needed will also help the request.
A hardship request is a one shot deal. You request and it is accepted or denied. So you want to put effort into the package to make it strong up front. There is no appeals process hardship request.
2) Last time it happened was in the early 90's during the downsizing after the gulf war. It could happen again...but I have not heard of it yet. I think the services are still waiting "shoe to drop" on budget issues before they start to downsize. Understand that we are still at war in Afghanistan and now they are talking about Iran....
I would not expect anything until the presidential election is over.
I have not heard of a "year early program". But in the mid 90's there were several different early out programs...that was a huge reduction in forces. It sure could happen again, particularly if someone like Ron Paul is elected.
3) Convince the command? That is the key. If you can convince your battalion commander
to let you out, they can make it happen.
It may be a sort of "hybrid"...say hardship issues, combined with a desire to start school, and need to leave
The convenience of the government is really a catch all. And it starts with your immediate chain of command. If you can show them you need to get out and letting you out early is the right thing to do you have a shot.
But understand it is rare. VERY rare soldier to be discharged early unless they have some reason under the chapter. So this one is unique. IT really comes down to convincing your chain of command to help you.
Frankly, if you have a relative with cancer, I would press this and add your other reasons to the mix. If your commander is behind your hardship request that is MUCH more likely to be approved then trying to convince them to give you a convenience of the government discharge.