1. Soon after you reach a safe altitude. you can start to retract your flaps to improve your climb performance. For a sea-level airport, the altitude is maybe 1000' AGL or even as low as 800' AGL. It all depends on the terrain.
2. There will be a caution message to warn the pilot if anything goes wrong. the leading flaps for 747 can be actuated with pneumatic power in normal mode and in electric power in secondary mode. For training edge flaps, it can be actuated with hydraulic power in normal mode and with electric power in secondary mode. The transition from normal mode to secondary mode is automatic.
Since there is a demand pump to support the main hydraulic pump, it is very unlikely to lose all hydraulic power for any system.
3. The bursting of 7 tires will significantly reduce your capability to stop the airplane, furthermore, those wheels spin at high speed with a loose thread that may damage piping or electric wires, thus disabling the airplane even more.