There's no precise walkthrough or correct move for this game, nor is it obvious. The door you need is randomized every time. As to which door? The angel/devil can provide a hint as to the puzzle. You may notice something about the three numbers they have and how they are related. The fractions are also a clue.
If you miss a few times, which is really only expected for the first bit, you can hit the side room, which has 30 doors.
After about ten tries, you should be able to sort what some fingers do and what the heads/tails and rock/scissors/paper combinations do.
If you chart out what goes where, you may find each attribute of the lonely statue has different values. The fingers are probably the easiest. With heads/tails and rock/scissors/paper constant, you'll note the differences are multiples of 6.
thumb=6 index=12 middle=18 ring=24 pinky=0
rock=10 scissors=20 paper=0
heads=15 tails=0
Add these up and modulo 30 and there is your answer.
The door in the other room has 7, 11 and 13 different possibilities, and 7*11*13=1001. Take away door 1001, and you have 1000 possibilities. The numbers are sticky here, but you can also extrapolate the strategy from the easy room.
The notes are potentially easiest once we know what to do.
A=143
B=286
C=429
D=572
E=715
F=858
G=0/1001
Saggitarius=77
Capricorn=154
Aquarius=231
Pisces=308
Aries=385
Taurus=462
Gemini=539
Cancer=616
Leo=693
Virgo=770
Libra=847
Scorpio=924
Ophiuchus=0/1001 (yes, it's a new Zodiac, potentially apocryphal.)
Goalie=91
Right Full Back=182
Left Full Back=273
Right Half Back=364
Center Back=455
Left Half Back=546
Right Winger=637
Inside Right Midfielder=728
Center Forward=819
Inside Left Midfielder=910
Left Winger=0/1001
Add up, modulo 1001, and you're done.
P.S. I can't tell you how to solve Petals of the Rose. Google it if you want, though it'll take some searching. Most of the first results are other people who don't want to give it away right away.