Is changing an old air filter necessary? Can I rather just be cleaning it?
The only ones you can clean are ones like K&N etc. Yours is likely a regular paper filter, so if it's dirty, yes replace it, they're cheap
Replace it. I even replace the reusable filters when the time comes. Small change for clean air for the expensive engine.
If you have normal air filter and it is dirty, just change it. It is cheap.
Within the lifetime of a paper filter it is ok to shake out some the the big nuts and twigs, especially if you drive in dirty conditions frequently. However, over time the smaller particulates are going to reduce performance; you should still change it on time. This is especially true for cheaper filters that may have lower surface area.
Just change the air filter. Same goes for the cabin air filter.