WH40 water heater timer: Does black wire from service box go to terminal #1 and black wire to water heater to terminal #2? Does neutral (white) from service box go to terminal #3 and neutral (white) to water heater go to terminal #4?

You posted 2 questions.
Add a comment to clarify problem
One question says black wire is sparking is inside water heater, and this question says black wire is sparking inside the panel and is posted under WH40 water heater timer.

If wire is sparking, then it is not attached firmly, or wire is not attached correctly, or there may be too many amps drawn across the terminal.
WH40 has 40 amp terminals and will handle all residential water heaters.

Open following links for instruction how to avoid sparking, and avoid fires inside timer:
http://waterheatertimer.org/How-to-troubleshoot-Intermatic-timer.html#fire
Open following link to see how to apply wire nut:
http://waterheatertimer.org/How-to-twist-electric-wire.html

Intermatic phone number: 815-675-7076

T104RT3 has 120Volt 300 watt transformer with 12-13-14Volt output.

The timer mechanism is 240Volt T104M.

Since both 120Volt and 240Volt are needed, the wire coming from breaker box should have 2 Hots and a neutral, plus the ground wire.
So you need 12-3 with/ground wire or 10-3 with/ground wire.
See image of typical wires plus ratings:
http://waterheatertimer.org/Color-codewire.html
See example image showing 2 hots and neutral and ground coming from breaker box:
http://waterheatertimer.org/images/Basic-240-Volt-water-heater-circuit-2.jpg

The 2 hot wires come from a 240Volt circuit breaker.
The neutral comes from the neutral busbar, or can be accessed from tying into any white neutral on nearby 120Volt outlet.

How to wire timer:
Connect 240Volt hot wires to terminals 1 and 3 on timer. Connect 240Volt timed output to terminals 2 and 4 on timer.

How to wire transformer:
Connect 120Volt transformer two different ways. (a) white wire connects to neutral wire and black wire connects to terminal 1 on timer. With this wiring, the transformer is ON at all times. (b) white wire connects to neutral wire and black wire connects to terminal 2 on timer. With this wiring, the transformer will be ON when timer turns on.
Do not put both stranded wire and copper wire under same screw terminal. Instead connect transformer wire to solid copper wire using wire nut.

Line voltage is not known.
240Volts has 2 hot wires and no neutral wire.
If both 10-2 wires test hot to ground, then you are working with 240V and no neutral is present.
http://waterheatertimer.org/240-v-water-heater-circuit.html#120-240

ET104C timer is shipped default setting for 240Volts.
ET104C can be wired many different ways.
Terminals 1 and 2 are for running the timer operation. So power lines connect to terminals 1 and 2.
Terminals 3 4 5 6 are dry. They have no power when wires are connected to terminals 1 and 2.
Typical 240v ET104C wiring shows next image.
http://waterheatertimer.org/images/ET-water-heater-circuit2-40.jpg

1) Yes, the noise is from clock motor turning the gears.
When timer is new, parts have a bit of white grease on them.
Turn off power and spray WD 40 or apply some white grease and see if that helps.

2) Yes WG1573 240Volt clock motor is going bad.
Tip out mechanism using thumb spring located top inside box and check clock motor number.

Buy WG1573 240Volt clock motor and extra trippers from Granger number 1PNK2
http://www.grainger.com/Grainger/timer-accessories/timers/electrical/ecatalog/N-8hi

http://waterheatertimer.org/How-to-wire-WH40.html

Notice on image below, there is a bit of white grease on lever.
This photo is from new WH40.

If this is new installation, you have Load wires and Breaker wires reversed.
http://waterheatertimer.org/How-to-wire-WH40.html
http://waterheatertimer.org/images/WH40-water-heater-circuit-5.jpg


Hot wires from breaker connect to terminals 1 and 3 ... notice also there are small white wires connected to terminals 1 and 3.
Small white wires go to 240Volt clock motor located on back of mechanism, so these terminals have to be Hot all the time so clock motor is ON all the time >> thus hot wires from breaker connect to same terminals that have small white wires.

Load wires to water heater connect to terminals 2 and 4

Reverse your wires and things should work fine.

EH10 has four screw terminals: 1 2 3 4
EH10 has two screw terminals exclusively for electronic clock motor.
These terminals connect exclusively to clock ... there is no internal jumper that passes power to another terminal.

Terminals 2 and 3) Black Hot lead connects to two terminals. Hot connects to terminal 2 and to terminal 3 ... so you put a jumper wire between terminals 2 and 3.

Terminal 1) All neutral or white wires connect to terminal 1, so there are two white wires on terminal 1.

Terminal 4) Black wire going to 120V Load connects to terminal 4.

Contrast EH10-electronic-timer with T-101-electro-mechanical-timer. T-104 clock motor has two separate wires that connect to terminals A and 1. Electronic clock doesn't have those separate wires.
http://waterheatertimer.org/images/Back-of-WH40-2b.jpg
http://waterheatertimer.org/How-to-wire-T104-Intermatic-timer.html#T101

Your second question about closing the circuit.
When timer turns ON, it closes circuit between terminals 3 and 4.
So the Hot is closed.
Neutral is not closed, it is open at all times.
EH10 is SPST timer ... One single pole is opened-and-closed (SP), and timer completes action with a single throw (ST)

Good choice for 120V water heater.

Black Hot wire from breaker connects to terminal 2.
Put jumper wire from terminal 2 to terminal 3.

White wire from breaker box connects to terminal 1
White wire going to water heater also connects to terminal 1

Black wire going to water heater connects to terminal 4

add a comment if you have more problems.

T104 timer is for 240 Volt circuits. It has internal 240V clock motor. Clock terminals and timer terminals are connected, so there is no way this timer can control 110V circuit.
http://waterheatertimer.org/How-to-wire-T104-Intermatic-timer.html

T101 timer is for 110V circuit.
T101 has 110V clock motor
Both white neutral wires = terminal A.
Black hot wire from breaker box = terminal 1
Black wire to load = terminal 2.
Grounds = green screw
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T103 timer is for 110V circuit
T103 has 110V clock motor
Both white neutral wires = terminal A.
Black hot wire from breaker box = terminal 3
Black hot wire to load = terminal 4
Grounds = green screw

T1905 timer is for 110V circuit.
T1905 has 110V clock motor
Both white neutrals = Clock terminal
Black hot from breaker = COM
Black to load = NO [load comes on when timer turns on]

make sure you purchased nthe correct timer and not a 220 volt timer for water heater use , you could still turn on and off manually but you would need 220 volt to run timer may sound silly but i have seen it several times before , look on the door plate and be sure it is a 120 volt 1 phase tmr motor

Shut off breaker to you water heater. STILL TEST FOR VOLTAGE BEFORE YOU TOUCH ANY WIRING. The 3 wire that go to you water heater disconnect them. You are going to install them to your WH 40 timer.
The wires that you disconnected will now go to terminals: Black to Terminal 1 & White To Terminal 3, The Ground copper wire will go to the ground terminal should be a green screw.
You will have to buy some 10/2 wiring to go from your timer to your water heater. You can buy it by the foot at Lowes. Figure how much you will need.
With the new 10/2 wire install the Black to terminal 2 & White To Terminal 4, the ground wire will go to the ground screw with the other ground wire.
Wiring that went to terminals 2 & 4 will be installed to you water heater, the same way when you disconnected them. Set your timer clock and your done. Turn breaker back on!