I want to start feeding my parakeet other things beside it's seed food from PetSmart. I don't have a spare dish to clip on the cage at the moment, until I get the extra cash in a week or so, but for now, could I just clean a small container, like possibly an old applesauce container, and set it in their for the time being?

I'm also wondering what sorts of things to put in their, and can I mix apples with carrots? and etc..

You can use any clean dish for a food bowl. And yes, you can put in apples and carrots(grated). They also like lettuce a lot.
Here are safe fresh foods for budgies
apple, grape, guava, kiwi fruit, mango, melon, nectarine, orange, peach, pear, pomegranate, plum, strawberry, tangerine.Peas, Broads beans, french beans , Broccoli, carrot, sprouts, cooked cabbage , kale.

pets question and answers,www.5d2d.com

They like sprouted seeds too.
Never feed apricot, avacado, Acorns

Here is a link on what NOT to give them.
http://www.avianweb.com/toxicfoods.html

My four budgies and 6 budgie eggs

If you want to make it easier on yourself, you can skip the dish all together. One thing that i find one of the best tools around the cage are clips. I had a few of those clips that you would use to close open potato chip bags and i just clip different types of fruits and veggies to the cage roof or side of the cage, near one of ur keet's perches. Personally, mine love stalks of broccoli and small carrots. Just be sure to wash them throughly first.

You can use any clean dish for a food bowl. And yes, you can put in apples and carrots(grated). They also like lettuce a lot.
Here are safe fresh foods for budgies
apple, grape, guava, kiwi fruit, mango, melon, nectarine, orange, peach, pear, pomegranate, plum, strawberry, tangerine.Peas, Broads beans, french beans , Broccoli, carrot, sprouts, cooked cabbage , kale. pets question and answers,www.5d2d.com

They like sprouted seeds too.
Never feed apricot, avacado, Acorns

Here is a link on what NOT to give them.
http://www.avianweb.com/toxicfoods.html

You can use any clean dish to feed your parakeet. They like green celery tops which you need to rinse well. They even love the water that clings to them. I've never given our parakeet carrots, though it may be fine. They also love apples.