On the 747-200, it's all about weight. If you are light enough, you can probably do the whole takeoff on 2 engines
And of course, no obstacles (because then the t/o path would have been calculated to clear them with 3 eng).
Last sim I practiced 340ton, end #4 fails at v1+, eng #3 fails at gear retraction.
If the secone engine fails after the gear is up, it is managable in most weights. You just have to trade altitude for speed, or stay in the ground effect and accelerate. Since flaps are mechanicaly controlled, you can retract them in small increments as the airspeed builds up. I know the book says retract to flaps 1, but even if you get to 10 (heavy t/o is usually with 20) you will be fine.
Regarding braking, on dry runways your concern is avoiding overheating the breaks, and on wet or worse you can brake as hard as you want - and on some cases you will need to.
Our company SOP is on dry: use MIN braking if possible, then Idle Rev is allowed. On wet: use MED and full rev. On contaminated: use MED and full rev, and if the actual runway length available is longer than calculated required distance + 15% company resereve by less then 1,000', then we use MAX braking.