You... can't make our own gym. In any official Pokemon game so far.
Increases wild pokemon encounter rate
You need to complete Pokemon Sapphire and Diamond and in Diamond you will need the National Dex. Go to the title screen of Diamond and press Start, then choose "Migrate from Sapphire" and follow the instructions. Choose the 6 Pokemon you want to migrate to Diamond, then confirm your choice. The 6 migrated Pokemon will be in the Pal Park and can be caught with 100% catch rate.
Slateport city on the northeast side. He'll rate your pokemon's name and change it for you if you want.
Try the grass on Route 117 outside of Mauville City. Roselia has about a 30% catch rate there.
Aron can be found in Granite Cave in all floors in Pokemon Omega Ruby and Alpha Sapphire. Since its catch rate is 180 out of 255, it can be really easy to catch using a Quick Ball or Poke Ball.
You can catch a Rayquaza by migrating it from Pokemon Ruby, Sapphire, or Emerald to the Pal Park with 100% catch rate. But the only other ways are to trade for it or use a cheating device such as an Action Replay.
I hope you mean "Staryu" when you say "satyru" since I'm basing this answer on the Pokemon Staryu. You need to use the Super Rod in Lilycove City. It's occurence rate is "common" so it should be pretty easy to capture.
You're team is decent.
It is an item that if you keep it in the treasure bag it will make the rate of Pokemon recruitment chances go up in dungeons.
First of all you will need all 7 Items for the highest success rate, Some arerequired like Surf and others like waterfall you can do with out it might justtake a lot longer.Acro BikeOld rod or Good rodA Pokemon with SurfA Pokemon with WaterfallAll 8 BadgesA Lot of TimePatience
Relicanth is notoriously hard to catch. It is possible, however, to get on in the underwater-seaweed areas outside and around Sootopolis City. It may take a while to get one, but be patient. They are there, but only have a 10% find rate.
Look at it this way, if you try catching Kyogre ( full health, no status changes, and no master ball.) with a regular poke'ball, you will catch it right off the bat! your welcome.