Ah Gerudo. Though a bit barren, it is one of my favorite sections of the game. Allow me to give you all manner of advice. And if you are using a phone and want to read the spoilered text below than just hit the quote button for my post and you can read it all in your reply box that way.
As you know, there is a merchant that has been able to sneak in at night. So, you may have already triggered this person's appearance but to be safe you may want to go back to the entrance of Gerudo City again the next time nightfall occurs and talk to the merchants outside the city as one of them will mention about waiting for this person or knowing they make the trek from the Kara Kara Bazaar to Gerudo City at night. Once you've spoken with them, head back to the Kara Kara Bazaar. At the Bazaar, there is a tall building that sells arrows inside. Search around there.
As for getting to the Divine Beast, settle in. It will be awhile. Even when you finally gain entrance to Gerudo City, you are going to have to go on another mission first. The key to the Divine Beast is through Riju, the leader of the Gerudo. Also, Gerudo City is one of the 3 great towns in the game along with Kakariko and Hateno. There are a lot of people inside and there are a whole lotta sidequests that they've got for you and I do recommend completing them for one of my favorite rewards in the game. In any case, enjoy your time in Gerudo City because it is packed with all kinds of interesting characters and moments.
As for your Tremors Sand Beast Molduga, he's pretty easy but it took me a couple tries to figure him out. When I was watching my Hero Journey played out on the map, I was surprised at how much I died in the Gerudo region because I don't remember getting killed there much but, I guess all the Lizalfos and electric bats did do a number on me as well as the Sand Beast a couple times. Anyways, if you want the strategy I know (and I think is the only way to fight this beast), I would hurry over to a solid rock in the area that I can stand on since the beast is unable to come up from under one of them. Then I would get a round bomb via the Sheikah Slate and throw that onto the ground ahead of where the beast was moving. The beast would sense the bomb moving on the surface and jump up swallowing it. Once in his mouth and him in the air, I'd blow up the bomb. This would stun him for a bit allowing me to attack him for a little while before he got his senses. Once he was moving again, it was back to my rock and repeat until he was taken out.
As for the Rito Village Divine Beast, near the top of the village maybe about 3 or 4 huts down starting from the Village elder at the top, there should be a hut with a Rito lady who talks about her husband going to the Rito Target Practice Area just over in the Hebra region. The game would have cinematically focused on the spot you need to head to in order to find him. In any case, it isn't that far to go. Across the lake the village is surrounded on at the North side of the lake is a shrine and close to that shrine is the Target Practice Area. That should allow you to pick up the trail onwards to the Divine Beast.
Finally, if you are trying to do some rupee farming, one area I learned about early on when I was playing the game but only just recently got to last week is a place called Pondo's Lodge. A lot of people listed it as the best place to earn rupees fast. It's in the Hebra region which is a place I avoided to keep some areas fresh for exploration and because I was never in a hurry for rupees. I took my time exploring and collected a lot of gems and treasure chests so I didn't have to grind (or feel like I was grinding) for rupees but if you want to do that then this is probably the best place.
You don't have to go far in the Hebra region. Pondo's Lodge is right be the Sheikah Map Tower that displays the Hebra region on your map. It's a bowling minigame. You lift a snowball and throw it down a hill and try to knock down 10 pins. It costs 20 rupees a try but if you get a strike on your first throw then you get 300 rupees and can get 100 rupees if you make the spare. The tip that I knew of when coming to this area is that you have to throw the snowball from where Pondo is standing and looking when the minigame begins. I tried it from throwing behind him but then I found better success by standing Link right in front of Pondo and getting him to face / look in the same direction forward and then throwing the snowball. Doing this, I was able to figure out a spot geographically that I needed to aim and throw the snowball and could start getting strikes on my first throw with ease. I think if you go with this advice you should be able to figure it out too and could start racking up more rupees if you need them.