If you desire to be reimbursed for lost wages upon any settlement, you need to make sure that you get a doctor's report indicating you cannot work due to your injury, documentation from your employer, and pay stubs or better, W-2's. If you work 'under the table,' you likely will have extreme difficulty getting this portion of your claim paid.
You need to notify your adjuster that you have lost time from work. You need to substantiate the amount of wages you have lost. A letter from your employer, along with an old paycheck stub, should suffice.
Individual policies differ on what they will cover, so lost wages might be excluded. You would have to check your policy. However, if there is no exclusion, then you can include them. If you are making a claim on someone else's insurance, you can claim them either way.
Yes you can include loss wages on an insurance claim if you can get a doctor to say that the injury made working impossible in your chosen field. If the insurance company refuses to pay you may need a lawyer.