Letting budgies out and branches?

I have two budgies that live in a large cage. I want to let them out more often (every day) because they are only out a few times a week. They are currently in the hallway, and if I let them out I have to constantly check if all the doors are shut so that they don't fly into the toilet or kitchen etc. There are no suitable rooms in my house for them to fly around in apart from my room, so I would like to move them there. I have heard and read that budgies like to be around sounds and things moving around, but my room is at the end of the house, and I only go there to sleep and do homework, would the radio be enough to entertain them? Or do they prefer other things moving around them? When I let them out of the cage, I put a perch on top of the cage and a couple of toys on, I also give them easy access to food and water. Is that ok? When I let them out, they don't really do anything, they just sit there, and sometimes eat the food. They are not hand trained, so they are weary around people.
Also, I am going to go to my friends farm, and she said that in the forests on her land there are many gum trees. If I got some sticks and branches from there for my budgies, would I have to prepare them? I have been told to bake them and wash them in bleach, but is that necessary if they are from a tree that grew in Australia? If budgies can safely chew the wood on these trees in the wild, why do I have to clean off the bark and kill everything inside the wood? I have not really researched about the parasites or bacteria that are supposed to be killed so what I am asking is probably really stupid but I would like to know why I have to anyway... If I have to bake them, what would I do with a big branch that doesn't fit into an oven?
Thank you

If it is very hot outside, you can put the big branch in the trunk of a car for a day. Of course it has to be HOT outside to be hot enough in the trunk to kill any creepy crawleys.

This is what I'd be most worried about my birds getting. It says can be spread by faeces so you'd want to wash any wild bird poo off anything you gave to your pets. I don't know enough about it to know how or if the virus is killed by heat. You might be able to find some more info online, or somebody on here might give us some better idea.
https://en.wikipedia.org/wiki/Psittacine_beak_and_feather_disease.