I don't have any of the items for my next recipe yet. I am just trying to plan and prepare, therefore I do not know a packaging date or anything.
I will be manually shaking.
My next questions are:
Does 1.63L represent the amount of water I need for the wort, or does it represent the water + the DME I use in it?
1.63 liter represents the amount of starter wort. 1.6 liter of water + 178 grams of DME. As a rule of thumb you could use 1 part DME to 10 parts water (by weight). In your case, 160 grams of DME in 1.6 liter (1600ml = 1600gr) water, which comes out to a gravity of 1.037, which is fine too, or even recommended.
All yeast projections are estimates. There is at least 10-20% error involved, either way, possibly more depending on packaging of the yeast, storage conditions, etc.
There's no need to work in 2 decimals (1.63 liter). 1.6 liter is fine enough.
If your yeast is older than the 1 month example given, you will need a larger starter to build more cells to end up at your target pitch of 185 billion cells. Most LHBS' yeast is 2-3 months old on average. The packaging or manufacturing date is stamped on the package.
If you're serious about brewing and using liquid starters, you really should invest in a stir plate, or build one. Lots of examples and instructables around. $10-15 in parts + some handiness.
I'm again pointing to using a drop of Fermcap-S to prevent blow off.
Boil your starter wort in a stainless pot and let cool with a tight fitting lid on it. When cool, pour into your 2 liter flask or other well-sanitized container, such as a clear glass growler or gallon "carboy."
Before you dive in , please inform yourself and read up on making starters. Plenty of information around, although some may be incorrect. You'll see.