Today I was going downhill a little on a narrow street when I notice a dog-leash and had to make a relatively quick full stop. Even though I was sitting with all my weight, the front brake definitely lifted the rear wheel.
I tried the same on the flat later on. I just pulled the level on full speed and the rear wheel came off the ground again.
When I go that fast and do a skid, I start fishtailing with or without rear-break.
Would a rear-break still help me stop faster?

yes

so would doing a 'bike throw' and shifting your weight back behind the seat.

Uh oh... I see another brake debate in the near future.

Fishtailing is the number one reason not to use both brakes at the same time. If you are grabbing the front brake hard enough to lift the rear wheel, you are using it correctly (maybe even a bit too much) and there's no reason to add a rear brake unless you want the redundancy in case of a front brake failure.

The fastest way to stop on an upright bike on dry pavement is to pull the front brake hard enough that your rear wheel is about to lift off the ground. To get more braking power, put your weight as far back as possible to avoid lifting the rear wheel. Because once it gets airborne, your center of gravity changes and you lose stability, making it easier to flip over.

fixed.

Riding on the sidewalk? Fixed or free?

I hate phonics.

on the street and it's fixed.

yeah don't ride on the sidewalk... the most dangerous place for you to ride

Did you really need to ask this question?

Legit. Think about what you're asking.

Two brakes will - rather obviously - help you stop more effectively than one.

The minimum stopping distance is achieved when 100% of the braking force is transferred to the front wheel, in which case a rear brake provides zero stopping force and is unnecessary. A rear brake is only necessary in slippery or poor traction conditions, or on extemely heavy bikes descending long or steep hills. On a FG, a rear brake is a detriment in slippery conditions, as better rear braking control can be achieved by backpedalling.

Go brakeless and you wouldn't have brake problems.

Just sayin', bro.

TT - sounds to me like the OP doesn't know how to effectively backpedal. Two brakes would definitely be an improvement in that case.

Wait - will eating two sandwiches make me fatter than eating one?

IMHO two brakes will help on a long, fast downhill, but not on a level maximum stop.

Interestingly, to me, I have formerly ridden with a Cane Creek Super Light single-pivot brake in front, and it did not have the power to really stop the bike, but, it would also not put me over the handlebars.

That particular inadequate front brake started me learning how to back pedal; and, as a result, I learned more about back pedalling than I had previously imagined existed.

If only you're eating them on a long descent and a dog must appear out of nowhere; making you shove both sandwiches into your mouth simultaneously.

Otherwise, you're good to go.

Phew!