After starting with 5 gallon batches, I have been brewing 2.5 gallon batches for the last handful of years - I have found this is the sweet spot for me between having a variety on hand and 'reward for effort'. I tried 1 gallon batches for a little while but that was just not enough.
1) bobeer and rodwha already answered.
2) The amount of water you start with depends upon your brewing method (extract vs all grain), how much you will leave behind in the kettle when you transfer to the fermenter, and finally on how much you leave behind in the kettle fermenter after you bottle or keg.
- When you transfer from your fermentor to your keg or bottles you will leave behind the trub (sediment at the bottom of the fermenter) this will cause some loss. The actual amount will depend upon your batch size, fermenter, and amount of dry hops added. Best way to figure this out is simply through brewing and observing how much you lose when you package your beer.
- After your boil, if you dump everything into your fermenter your trub loss or kettle loss will be zero. Some brewers try to leave as much of the trub behind in the kettle, if you do this you will have to factor the amount left behind into your water lost during the process.
- If you are brewing extract batches, your main loss of water will be boil off. To calculate your boil off rate boil a gallon of water in your kettle - the difference between what you started with and what you ended with is your boil off rate.
- If you are brewing an all grain batch you also have factor in water that is absorbed by the grain during the mash.
I recently started using an electric all in one system (Anvil Foundry) so I have been trying to zero in my process losses. For my last batch I used the following:
I started with 4.00 gallons of water and lost about 0.35 gallons due to grain absorption, this left 3.65 gallons in the kettle for my boil. During the hour boil I lost about 0.50 gallons leaving me with 3.15 gallons. After chilling the wort its volume was closer to 3 gallons, I then transferred 2.75 gallons to my fermenter and had approximately 0.25 gallons left behind in my kettle.
So, 4.00g - .35g(grain absorption) - .5g(boil off) - .15g (shrinkage) - .25 (trub loss) = 2.75 gallons in my fermenter.
Then when I keg this beer, I know from past experience that I will leave roughly 0.25 gallons of trub/beer in my fermenter, so 2.75 - 0.25 (trub loss in fermenter) = 2.5 gallon in my keg.
Using software like Beersmith or Brewfather will make these calculations much easier (both have free trial periods for you to play with).
3) For my 2.5 gallon batches I primarily use 3 gallon plastic carboys but do have a few 5 gallon ones. Too much headspace can impact flavor in some beers. If I do have to use my larger carboys I make sure not ferment any NEIPAs or other heavily hopped beers due to oxygenation concerns (larger head space will definitely lead to more oxygen in the fermenter. For the same reason, I do not like to use the larger carboys for lagers or other longer fermenting beers. Having said that, don't worry too much about it - maybe stick to a fermenter 20% larger than what you are fermenting or the 2-3" rodwha mentioned above.
4) Best way to store an opened bag of hops is with as little oxygen as possible and in the freezer. I use a vacuum sealer and like to put the original foil bag in the plastic vacuum bag when I seal it (I think I picked that up from a post on here). If you do not have a vacuum sealer, try to squeeze as much air out of the foil bag as possible, roll it up and tape it shut and still store in the freezer. As for yeast, you will be fine pitching a full pouch into a 2.5 gallon batch. If you do want to save yeast (and thereby save some $) you can make a starter and pitch some and save some. I usually make a 2L starter, when it is done I put in the fridge, decant the beer and split the yeast into 4 mason jars - each one is generally good for one 2.5 gallon batch.
Sorry for the long winded answer!