Batch size is the amount wort that goes into your primary.
10.0 gallon capacity kettle
7.00 gallons at 60 min. (boil start)
6.00 gallons (post-boil volume)
5.50 gallons after transferring to primary (batch size)
5.00 gallons (bottled)
There are certainly benefits to not making a concentrated wort and then topping it off with several gallons of plain water. I would recommend getting into the habit of full volume boils. For a full volume boil, you have to know how much boiloff your particular system yields, take into account how much wort is absorbed by the hops and the grain, and also how much is lost to trub after transferring.
1.2 - 1.5 liters of water per lb. of grain is the typical average mashing ratio when using unconverted grains. So if you are mashing 3 lbs. of grain, then you want to use 3.6 - 4.5 liters of water for the mash.
Partial Mash is easy. PM me with questions. I've brewed over 100 partial mash recipes.