If you have excess to MyBoeingFleet you will be able look at the Boeing version of the 777 FCOM and FCTM. The take off flap settings are 5, 15 or 20 no mention of 10.
In the performance dispatch section of this FCOM only flap 15 runway charts are provided covering the -200ER GE90-76B iaw with JAR requirements(dry and wet runways) plus -200ER Trent 892 and -300 PW4090 iaw with FAA requirements(dry runway only)
Regarding the flap retraction speeds the FCTM states that all speeds are based on Vref 30. Therefore
Flaps 30 = Vref30
Flaps 25 = Vref25
Flaps 20 = Vref30+20
Flaps 15 = Vref30+20
Flaps 5 = Vref30+40
Flaps 1 = Vref30+60
Flaps Up = Vref30+80
Hope it helps
