To summarize,
The "gasket" you refer to is not supposed to hold fluid, it is just a mechanical interface and maybe a dust cover (plastic part). The slots at the bottom are so you can see the brake fluid is leaking, and to keep it from leaking into your booster (bad).
After changing the master cylinder, I would bleed all the brakes, until you get clear fluid and no air bubbles. See youtube. You should be doing that every few years anyway, maybe 6 yrs in Utah. Or if you switch to silicone DOT 5, you never need to.
Since a newbie, don't use a regular open-ended wrench to loosen the tube nuts or you will probably ruin them. Get a special "flare wrench" which better surrounds the nut.
Don't feel bad that you thought that part was a gasket. On many newer cars it is a vacuum seal. My 84 M-B is like that. The boosters on our cars have an internal rubber bellows which forms that seal, which you will see when you remove the MC. Good in that it keeps leaking brake fluid out of the booster, but bad in that the booster is thicker.
A final newbie tip. Glycol is an excellent paint remover, so quickly clean up any spills. Also why your firewall is probably rusty below the booster. Another reason many classic car owners use silicone fluid.