Howdy! Your cider is going to turn out fine. Really one of the more easier things to make. As long as your trash can is sanitized and air tight then you should be fine. I have no idea what type of liner (or any) that you should use because I don't have any experience with anything but regular fermenting vessels, but it should be ok.
Frankly I would do it all in smaller batches so you can control it better. Putting 50 gallons in a trash can would worry me about the contamination because you are using something that it wasn't designed to be, so I would do it all in regular 5 gallon fermenters. It really wouldn't take all that much extra time plus you can control the whole process so much better, a lot easier to carry, etc. Think about your back, man!!
As far as pasturizing the batch - you could heat up individual smaller batches to 140F or so and hold it there for about 20 minutes per batch at that temp, but I don't really think it is normally necessary. However since this is straight natural cider from the Amish, you might want to consider heating it up 3 gallons or so at a time. Obviously you can't do 50 gallons if you don't have the vessel, so improvise.
Here are some other quotes from threads I have found about this to hopefully help you out:
""Next, don't boil anything! Do not boil the juice (or if you do make sure you add some pectic enzymes or it will never clear). Second, do not boil the honey! Warm the juice and add the honey to dissolve by all means but there is no reason to boil! 120 degrees is fine to pasturize (I don't bother, honey is highly resistent to bacteria and the juice is pasturized if you get it from the store, if not, campden it 24 hours in advance).
Lastly, nutrients are not needed but I have found they still help with fermentation. For cysers I really like Lalvin 71B or Nottinghams (if you want to use an ale yeast). It is going to ferment dry no matter what you use (most likely) and you may need to backsweeten to get that apple flavor.
Basically, it should go like this. Apple juice to 5 gallons + yeast of your choice + honey (I would go with 6-7 pounds) + sugar to an OG of 1.12 or so. Ferment till primary is done (about 2-3 weeks). Transfer to secondary for 2-3 months. Then either keg it or age it (if you can wait, worth it) for six months to a year. Voila . . . Cyser!""
And another thread - http://www.homebrewtalk.com/showthread.php?t=2727&highlight=cider+pasturize
Hope those are helpful.