This is current version!

1)

Time delay between Cloak uses - ~ 15 seconds.
Time delay to repair Cloak - 10 seconds.
One timer affects another - no.

You see the issue?

2)

On normal difficulty, if you come to FTL beacon too late (its still on border, not red) already in first sector you have a chance to fight ship armed with 2x Burst Laser MK2 and 1x Heavy Laser. And this is purely through Luck roll. You gonna enjoy it!

3) See attachment about unoccupied exit.