I'm also a brand-new conure owner, so I'll let others with experience advise you about what precautions to take. But there are a few human engineering tips I can give you to make this safer while you're still living with your parents. (How soon are you moving out, by the way?)
Cookware isn't cheap, especially when we're talking about several pieces, so you might be right about your parents not throwing them away. Even if they promise to warn you before using the cookware, cooking is something so habitual that it would be very easy for them to forget. If they don't want to throw or give the pieces away, here's what I'd recommend:
- Provide them with alternate cookware! If it's just for a few weeks/months until you move, they might not mind using lower quality, cheaper pans. Maybe even borrow from friends/family - most people have extra pots and pans that they only take out a couple times a year, and would be willing to lend them to you short-term. Even if your parents aren't enthused about this idea, and even if they say they won't use the alternative pieces, make sure that they're at least available for convenient use "just in case".
- Ask if you can put the teflon in storage in the basement (or some other location out of the kitchen) until you move out. Short of throwing them away, this is probably the best solution if your parents are willing.
- If they insist on having them available for use: take all the teflon pieces and concentrate them in a central location (a box or cabinet). Label it with a reminder to warn you before using them, so you can take any necessary ventilation precautions. This will make it much easier for them to remember to warn you - especially if the location is a new one, that's outside their normal cooking routine.
Most of all, try to keep this issue from turning into an argument with your parents. The minute antagonism or defensiveness enters the conversation, they're much less likely to be accommodating. Use phrases like you used in your original post here: "I should have done the research first", "I know this is a big inconvenience for you", etc.
Saying "I made a mistake, and I know you're not obligated to help me, but..." gets much better results than demands, lectures, or even a simple polite request. Don't present their help with this as something you are entitled to, because that will automatically put them on the defensive. Especially since they're your parents, this could easily turn into a dynamic of "you should have known better, now deal with the consequences yourself".
Here's a general script you can use (not my actual opinion or judgement of you lol, just the kind of statements you should play up):
- Admit fault from the beginning, stress that you learned a lesson and that you'll think of these things in advance in the future. Turn it into an educational experience that's
already happened, rather than a lesson they need to help you learn.
- Then ask for their help: even though you
know it's going to be a huge pain for them, and they obviously aren't obligated to do all this (they already do so much for you!), but it would really help if they did.
- Obviously you'll do everything you can to make this as easy and convenient for them as possible (do all the necessary organization, labeling and purchasing yourself, bringing them breakfast in bed every day), etc etc.
- Yes, of
course you trust them to remember which are the teflon pieces and which aren't! You know you're being a little paranoid, but you feel very responsible and parental toward this bird, and you would feel horrible if anything happened. It will make you feel so much better if you could just move all the pieces to a separate cabinet and put a note on it, even though intellectually you know it's not necessary. Haha, you're sure that when you have your first child you'll be the same way, right mom and dad? (Fight dirty! Bring up the grandparent instincts!)
Good luck!
id really appreciate it ... im gonna talk to my parents about throwing out the pans but knowing them im sure they wont :/ 
