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Do you know what kind of wood the old logs are?
Not all wood is safe for budgies so it's important you choose carefully.
After determining a wood is safe, all wood you gather for use in your budgie's cage should be disinfected as indicated in the link below:
Bird; Birds: Safe, Toxic Trees, Woods. Safe Tree Wood. Parrots. Parrot cages.
Budgies like to chew and chewing safe woods good for them.
If you post a close-up in-focus picture of your budgie's beak, we will be better able to tell if the chipping on her beak is normal.
What sort of diet is your budgie on at this time?
Are the logs in her cage something she could potentially use as a nesting site?
It is not recommended you put anything in the cage that she might choose to nest in.
I have male budgies and two of them like to practically lie on their tummies when they rest.
In fact, I have a woven palm leaf platform which I call their hammock and one loves lying on his tummy on it.
The other was lying on his tummy on the patio the hammock hangs from. 
As long as your budgie is active, not fluffed up and is eating, drinking and pooping normally - I would not be overly concerned because she sometimes chooses to perch in a "tummy-resting" position.
Not all wood is safe for budgies so it's important you choose carefully.
After determining a wood is safe, all wood you gather for use in your budgie's cage should be disinfected as indicated in the link below:
Bird; Birds: Safe, Toxic Trees, Woods. Safe Tree Wood. Parrots. Parrot cages.
Budgies like to chew and chewing safe woods good for them.
If you post a close-up in-focus picture of your budgie's beak, we will be better able to tell if the chipping on her beak is normal.
What sort of diet is your budgie on at this time?
Are the logs in her cage something she could potentially use as a nesting site?
It is not recommended you put anything in the cage that she might choose to nest in.
I have male budgies and two of them like to practically lie on their tummies when they rest.
In fact, I have a woven palm leaf platform which I call their hammock and one loves lying on his tummy on it.
As long as your budgie is active, not fluffed up and is eating, drinking and pooping normally - I would not be overly concerned because she sometimes chooses to perch in a "tummy-resting" position.