My cherry head eats primarily a mixture of Kaylor of Colorado Sweet Harvest Cockateil no/sun seed, along with fresh sprouts, and fresh foods (rice, legumes, veggies, etc). She's not really big on the medium parrot food so this is why she gets food for smaller birds... she may occasionally eat some Zupreem pellets too... but rarely.
My mitred eats primilary Zupreem Natural Pellets (after switching him off of Zupreem Fruit Blend), a tiny amount of safflower seeds (now that he knows how to crack them), and whatever foods I eat, since he wont eat any of the birds fresh foods made for them (and I'm not particularly interested in it either!

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The seed mix that your conure is on probably is not the healthiest.... you need to see if there are any bird stores in your area, or look up some bird food retailers and find a supplier who sells conure mix foods. Not only that but he needs fresh foods daily.
Here's a list of foods that can be fed.... although it's not complete.... its from the Healthy Bird Cookbook which I recommend ANYONE to get!
Grains, Breads, and Muffins
Corn bread
Graham crackers
Mandel bread, soaked
Matzoh
Matzoh balls
Mini bagels
Oatmeal
Pastas
Rice
Rice cakes
Rice Chex
Rice Krispies
Sweetened corn cereals
Sweetened oat cereals
Toasted bread
Unsalted crackers
Unsalted, unbuttered popcorn
Wheat cereals
Whole-wheat or multigrained bread
Zweibach toast, soaked
Other grains
Vegetables
Beans
Beets
Broccoli
Carrots
Corn
Green beans
Jalapeno peppers
Lima beans
Mixed vegetables
Okra
Peas
Potatoes
Summer squash
Sweet Potatoes
Winter squash
Yams
Fruit
Apples
Bananas
Berries (all kind)
Grapes
Kiwis
Mangos
Melons
Oranges
Papaya
Pears
Star Fruit
Winter Squash
Yams
Other Foods
Hulled seeds
Millet spray
Monkey biscuits
Peanut butter sandwiches rolled in millet
Pellets
Scrambled eggs
Hard-boiled eggs
Sprouted seeds
Foods to avoid
Chocolate
Avocados
Sugar (too much is a bad thing... best kind is natural sugars)
Old Seeds
Mayonnaise products
Unwashed Fruits or Vegetables
Rhubarb (contains oxalic acid, as does spinach - feed only in small amounts)
Fruit Pits
Nuts (brazil nuts, almonds, imported nuts that have been polished/dyed)
Dairy Products (birds are lactose intolerent-feed small amounts-cleaned/cooked eggs and yogurt fine)
Mold
Caffeine
Salt
Alcohol
Food Dyes
Sulfites (found in dried fruits and veggies to help preserve them-only from health food store)
Don't expect him to talk. If you have expectations for a bird, you may not be capable of handling a bird... because that'll only lead to dissapointments... however, if you don't mind a bird being just that, a bird, however they learn to talk or any other desirable behavior, there will be no dissapointment! It's really up to the birds who they will be. They can be taught things, however just don't expect certain things of them. Really, the best thing here is to talk to your conure as if he was a child... i.e. tell him what you are doing, where you are going, how long you will be gone, ask him questions, point things out (i.e. teach him as if you would teach a child), etc. If he talks, then he talks! If not, don't worry about it!
As for swings... well some conures do, and others don't! Charlie is terrified of the cockatiel swing that I have, and Noel tends to dislike any unsteady perches (except for a swaying branch in the wind). They are all individuals, it's up to them.