iwamineshuu

Go to discord and type in !Whois <insertuser> in the #bot-commands channel

All Gym battles and all Battle Facilities. That's it.

I believe you can only find Articuno in the snow maps (22 & 23) and Zapdos in the Electric maps (16 & 17).
 
Check the pokemon location guide here:
https://wiki.pokemon-vortex.com/wiki/List_of_Pokemon_By_Location

Now if you still remember the email, for gmail you can click on "forgot password" and verify identity by phone. You'll then get a link to change it. After recovering your legit email, go back to vortex and click on forgot password and reset it.

Then I would advise to give Patrick or one of the admins a ring and ask them to check which email you used, then go to forgot password in the google accounts page and verify by phone to reset your password. Afterwards, you can come back to vortex and reset your pass for the game here.

Looking at your profile badges I can see you're missing a battle from the Alola Island Kahunas. That's why you aren't catching any legends. Try battling all the alola gym leaders again (Hala, Olivia, Nanu, and Hapu) and see if you get the green message now.

There's a few ways of earning...
 
1) You can refer to this thread for training your lower level pokemon:
You'll earn a decent amount of money after each battle. Usually over 10K if you train low leveled pokemon but at some point you'll earn way less once the pokemon is higher in level. For example level 100 pokemon usually get 3000EXP and around 1500 money per battle with the training accounts.
 
2) Frequently you'll be awarded money from daily login rewards.
 
3) If you manage to capture a rare pokemon, you can try selling on the auction house. The min price you can potentially get is 25K money per sell.
 
4) Or you could go the real world money route and actually buy mystery boxes from the Store. A box can typically give you anywhere from 25K to 1 Million.
 
5) Some people try offering EXP training for another player in exchange for money. It's a hit or miss really.

Unlike legendaries you can find starters without beating the gyms but it'll usually take a lot of grinding unless you luck out on the map or the odd auction house/trade. 
 
Adding on to @waybig you can also find vortex balls in daily login if you somehow get a lucky mystery box.
 
The other new pokeball is the beast ball which you can get from doing sidequests. It also has a 100% capture rate against ultra beasts.