Unlike in many of the other games, puzzle solutions don't change with difficulty here. The solutions are always the same.
Old Man's Hand
Use the chemical from the storage room on the statue in the science room, revealing the gold medallion. Use this on the clock tower.
Piano Puzzle
Amusingly, Konami put the piano puzzle solution on their original SH1 site. Apparently, enough people had trouble with it this was the ONLY puzzle solution on there; though they gave basic info on the number of endings, too.
Black birds relate to black keys, white birds to white keys. Five of the keys are broken, thus "without a voice," so only these ones are used.
First flew the greedy Pelican,
eager for the reward.
White wings flailing.
Then came a silent Dove,
flying beyond the Pelican,
as far as he could.
A Raven flies in,
flying higher than the Dove.
Just to show he can.
A Swan glides in to find a peaceful spot
next to another bird.
Finally, out comes a Crow,
coming quickly to a stop, yawning and then napping.
Who will show the way?
Who will be the key?
Who will lead to the silver reward?
Play the notes in order to get the silver medallion, then use it on the clock tower.
Clock Tower
After using the two medallions, go to the basement to turn on the generator in the boiler room. The clock tower door will now be unlocked. Go through it.
Plates Puzzle
Poem on the wall:
Clouds flowing over a hill.
Sky on a sunny day
Tangerines that are bitter.
Lucky four-leaf-clover.
Violets in the garden.
Dandelions along a path.
Unavoidable sleeping time.
Liquid flowing from a slashed wrist.
The colors associated with the things in the poem relate to the plates that need to be put in the holes.
Valves Puzzle
1. Left valve: turn right once
2. Right valve: turn left twice
Zodiac Puzzle
Input the numbers of limbs on each zodiac sign on the number pad below each to get the Stone of Time, which you can then use on the clock in the Antique Shop.
Grim Reaper's List
Names on the sign in order or age, last names spell "ALERT," which can be input on the alphabet pad.
3f Nowhere Doors
Use the camera on the paintings to get the solutions for the doors.
Cheat Sheet
Here's a black and white image of the cheat sheet I use for saving or printing out for reference.