Will I miss a lot of work if I have a diseased toenail surgically removed?

Depends. On your occupation. Most of the time you will not miss a lot of work.
No. Depending on the type of work you do and the type of shoes you have to wear you may miss no work or 1-2 dats.
No. Removal of a toenail is a simple procedure and usually performed using only local anesthesia. Depending on how much walking you do for your job you may only need to be off 1 day. If the doctor is going to remove the growth plate of the nail this may require more sedation as well as local anesthesia. There will be more time needed off work perhaps 3-4 days.