How do you get Super Saiyan 4 Goketa?

I think you mean S.S.4 Gogeta, there are two versions to unlock: Goku AND Vegeta. I will list them both for you. Goku's is unlocked in the process of unlocking Omega Shenron, so read carefully:

Broly: This guy is a pain...but he's still fun to use...as usual, you need to use Goku's Dragon Universe for AT LEAST the second time. Now, get to the Majin Saga, the point where Goku is looking for a person to fuse with. After Gohan is absorbed, look in the surrounding area (where Goku starts this stage), for a ??? nearby. After the scene with Hercule, heda towards the red dot, BUT DO NOT START THE BATTLE WITH SUPER BUU!!!!! Close to the dot, will be another ???.

After the scene with Tien, search the surrounding area once more, this time for a spot labeled "Mountains". After you talk to Kibitoshin, go and fight Super Buu. After Super Buu has been beaten for the second time (the fight within his body), a new red dot will be on the map. BEFORE you go to this new battle, search the islands to the East/right of the World Martial Arts Tournament. If you find the correct one, you will unlock the S.S.4 capsule for Goku.

Now go to the red dot. If you beat Broly, he will become unlocked. You can battle Broly with Vegeta, but the sequence is slightly Different. Before you fuse with Goku, go to "Ice Island". After talking to Kibitoshin, go fight Buu. The "broly Dot" will appear later.

Omega Shenron: First: you must fullfill the "Broly Requirements" listed above, only after Broly has been defeated, ignore the red dot and go to West City. After the conversation with Bulma, go and beat Gotenks at the tournament (this will unlock the Gogeta Fusion for Goku). After your battle, a new red dot will appear...Omega Shenron. When you arrive, S.S.4 Vegeta will show up. The two of you will fuse to become, and unlock, S.S.4 Gogeta. If you beat Omega Shenron, he will become unlocked. NOTE: You will be able to defeat Omega Shenron easily in the transformed state. If you run out of time, and change back into Goku, you are so F**ked!!! Try like hell to use the 100X Big Bang Kamehameha, it will put a serious A**-Whooping on him!!!

S.S.4 Gogeta: Use Vegeta's Dragon Universe for AT LEAST the second time. Fullfill the "Broly Requirments", DO NOT go to the battle with Broly after the second battle with Super Buu. Slowly fly over the islands in the bottom-right of the map. When you fly over the right one, a scene will automatically triggered. After the scene has ended, go beat Broly. After Broly has been beaten, ignore the red dot and go to Baba's Palace instead. Carefully search surrounding area for a spot labeled "Plains". After you talk to Bulma, go to West City. After the West City scene, you will have the S.S.4 capsule for Vegeta (it also explains how he skipped S.S.3). Now go to the island with the red dot. If you defeat S.S.4 Goku, you will unlock the S.S.4 Gogeta capsule for Vegeta.

Supreme Kai: Use Gohan's Dragon Universe for AT LEAST the second time. After you have unlocked Videl, AND beat Goten, go to Kami's lookout and beat Piccolo. When the Dabura fight appears, go to the mountain area of the main continent. Find the scene with Vegeta, and then go fight Dabura. After the Dabura battle, Gohan will now go after Vegeta instead of Buu. Beat Vegeta, and head towards the red dot. BEFORE you fight Buu, use the "Sense Aura" (R1) to find the "plains" spot near Central City. After the scene with Supreme Kai, he will become unlocked.

No,...Gokule is not in Dragonball Z: Budokai 3

In order to enter a password into Dragon Arena, press R1/R2 (it's one or the other) when the "choose you opponent" screen comes up. If you never entered a password before, this screen should be blank. Now press either start or select to begin the process of entering a password.