Barking is not always a sign of aggression. First and foremost it's a communication tool.
To understand what your dog is trying to communicate in those "abnormal" instances, you need to interpret the vocal clues and body language.
A dog's barking is almost comparable to a human's shouting.
- Dogs bark to welcome people that matter to them like humans squee when greeting friends
- Dogs bark while playing and having fun like children scream in play
- Dogs bark to warn off intruders and agressors like police officers shout out to people during an operation
- Many dogs bark if they're insecure or don't know how to act in certain situations. This can escalate to real agression if you harass them, but most dogs try to move away and avoid a conflict rather than attack.
A happy barking is often done in a higher pitch and might be accompanied by whining.
An aggressive barking is often accompanied by visual clues and a gurgling sound.
The face of a dog tells a lot about whether the bark is agressive or not. Have a look at these examples. Can you tell which dog is agressive?
The body language of the dog in the first image is aggressive.
- He's pulling up his lips and wrinkling his nose to display his teeth as much as possible.
- His ears are pulled back and close to the head.
In the second picture the body language is not aggressive.
- You can see the lower canines, but the upper canines are hidden behind the lips
- The ears are pointed forwards, indicating alertness or interest
Your dog's behanvior
Most of what you describe indicates that your dog barks for attention.
Chewing at the crate most likely means that he doesn't want to be in the crate. He wants to interact with people or play and is frustrated at being sent into the crate.
Same thing when you drop an object near his crate. Falling / moving things are always interesting and he probably wants to at least sniff it, maybe even play with it. But he cannot reach it through the crate and barks either because he's frustrated or to prompt you to give it to him.
Cleaning the carpet can trigger a playful bark (because of the movement) or an insecure bark (our dog always barks at the vacuum, but it's not agressive and he wouldn't attack it).
What you should do
Analyze the body language of your dog. If he's actually agressive, you should do regular obedience trainings with him to assert your dominance over him. Under no circumstances should you cause him pain as punishment, because then he might learn to strike first before you can hurt him.
If his barking is not an expression of aggression (which is much more probable), you can choose to give him a toy like a Kong or food dispenser ball or a chewing stick to entertain him. Not every single time, but for example if you put him in the crate while having guests. This is like a consolence: you cannot play with our guests, but have a treat / toy instead.
Otherwise simply ignore his antics. If his barking doesn't yield the desired result, he'll stop soon enough.