The fact that you are asking these questions tells me that you need mountaineering classes and some experience with short winter camping trips to even begin to think about doing such a trip.
In short, it needs more than you currently have - a real solid sense of whether or not you can do the trip. If you have solid winter skills, you would not ask the questions at all.
If you can't afford going to Ireland, you probably can't afford to do the JMT - winter trips have an entirely different gear list than 3 season trips. A month in high elevation Sierra would mean 4 season gear, full mountaineering style, tent and crampons and all. Also very good routefinding skills. And you should not do it alone unless you have years of experience in winter mountaineering, and you don't mention any companions...
"In the beginner's mind there are many possibilities. In the expert's mind there are few." Shunryu Suzukihttp://hikeandbackpack.com