Hi first were do you find that key?

1) Key: Key can be found in Western Cavern, Solar Cave and Desert Region. But since you've just beaten the game, Western Cavern is not available. You can find Key at Desert Region at a low rate so I suggest you to go to Solar Cave. Make sure to bring a Pokemon can walk on water to get the HM Surf on 20BF (there is also a HM Waterfall on 15BF in a keyed chamber, you will have to unlock this chamber by facing the lock and use the key you found along your way to open it)
2+3) Legendaries and Dungeon: When you found HM Surf, a series of events will be unlocked. [SPOILERS STARTS] You will be able to confront Latios and Latias. Then you will see a Spinda collapse, and you will have to find the mirage Pokemon for him. This will allow you to fight Entei, Raikou, Suicune, Ho-oh in a series of dungeons. If you recruit Ho-oh you will go to Western Cave to fight Mewtwo. Recruiting 3 lengendary birds allows you to go to Silver trench to fight Lugia. After this Metore Cave will be unlocked and you will go and face Deoxys there. [SPOILERS ENDS]
Articuno: Frosty Grotto 5F (access through Frosty Forest without any rescue job, can only recruit after credit roll, auto Friend Area)
Zapdos: Mt.Thunder Peak 3F (access through Mt.Thunder without any rescue job, can only recruit after credit roll, auto Friend Area)
Moltres: Mt.Blaze Peak 3F (access through Mt.Blaze without any rescue job, can only recruit after credit roll, auto Friend Area)
Mewtwo: Western Cavern 99BF (can only recruit from the second time you complete this dungeon onwards, must have Friend Area Cryptic Cave in possession)
Mew: Buried Relic 36BF-98BF (appear in monster house or generated when you enter the floor, won't spawn and appear only once on each floor, must have Music Box in Bag, must have Friend Area Final Island in possession)
Entei: Fiery Field 30F (can only recruit from the second time you complete this dungeon onwards, must have Friend Area Sacred Field in possesion)
Raikou: Lightning Field 30F (can only recruit from the second time you complete this dungeon onwards, must have Friend Area Sacred Field in possesion)
Suicune: Northwind Field 30F (can only recruit from the second time you complete this dungeon onwards, must have Friend Area Sacred Field in possesion)
Ho-oh: Mt.Faraway 40F (can only recruit from the second time you complete this dungeon onwards, must have Friend Area Rainbow Peak in possesion)
Lugia: Silver Trench 99BF (Auto Friend Area)
Celebi: Purity Forest 99F (Auto Friend Area, no need of fighting)
Latios/Latias: Pokemon Square (complete Northern Range and Pitfall Valley dungeon, then both of them will ask to join, must have Friend Area Southern Island in possession)
Regirock/Regice/Registeel: Buried Relic (in order) 15BF/25BF/35BF (The parts that form Music Box which is held by these 3 Pokemon must be removed before recruiting these Pokemon, must have Friend Area Ancient Relic in possession)
Kyogre: Stormy Sea 40BF (Auto Friend Area)
Groundon: Magma Depth 3BF (access through Magma Cavern without any rescue job, can only recruit after credit roll, auto Friend Area)
Rayquaza: Sky Tower Summit 9F (access through Sky Tower without any rescue job, can only recruit after credit roll, auto Friend Area)
Jirachi: Wish Cave 99F (must have Friend Area Mt.Moonview in possession)
Deoxys: Meteor Cave 20BF (can only recruit from the second time you complete this dungeon onwards, auto Friend Area)
4) Friend Bow: You can get one at 30F of Mt.Faraway, home of Ho-oh. You'll need a key (Have a look at answer number 1). There is an alternate way to get it, you can buy it from Kecleon Stall at Joyous Tower for 5000 Poke.