When I'm in doubt...take them to a vet!
I take mine in for a well bird check when they first come home with me and quarantine them 'just in case'. If there is a problem you may be the one that saves this little bird!
The beak could be a number of things from poor diet to scaly mites. We can't properly diagnose that thru the Net, sadly. An intelligent guess is all we could manage but it's too important in this birds life for that!
As for 'Strange' sitting n sleeping positions, well that could just be the way he likes to relax or he could be having respiratory issues. Again we can't figure it out but a Vet can tell you right away.
I want to say one more thing. If anyone, including the vet says he's not worth treating because he's older or he's just a bird or he's just a Budgie you can tell them, with my permission, that he IS worth treating! Some vets, including bird vets don't feel Budgies, because they're so inexpensive, are 'Worth' treating. I've had it happen to me. It makes me really mad because Budgies are one of the most intelligent, loving, cool and valuable birds anyone will Ever be lucky enough to share their life and home with. I've had and/or worked with every kind of big and small bird you can imagine and wouldn't trade my Budgies in on any of them!
If you give us more info about how your bird's breathing, eating, how his droppings look and more pics maybe we can try and make some intelligent assumptions until you can get him to a vet.
Remember, a bird that's sick 2 days is like us being sick 10 days or more!
Let us know how he's doing! Get him to a vet as soon as you can!
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