(I can answer based on how my agency does things (note this may not and probably is not the same everywhere)
1. Do detectives really work in pairs (as on TV)? We work with a partner.
2. Do they use their own cars? Absolutely not!
3. If they use (unmarked) Department cars, do they take them home at night (when off duty) and can they use them as family cars when off duty/on vacation? We can, provided that we do not travel out of the county that my city is located in. The reason for this is that if we are on call, we have to respond to call outs quickly.
4. Do they keep guns in the boot (trunk)? No, we carry them.
5. If they do, are these guns held in the trunk overnight?Guns go inside the house at night.
6. Are these guns still held in the trunk if/when the cars are being use to collect the groceries? Maybe in with the spare tyre?
7. I'm assuming these unmarked cars (whether owned by the men or the department) have shortwave radios and sirens installed and detachable blue lights. Is that correct? Yes. Mine has all the above except a detachable light. I have lights that are mounted inside the car up around the visors.
8. Is there an exam for a uniformed/beat officer to become a detective? Not where I am. It depends on training, education, and experience.
9. Are detectives paid more than uniformed/beat officers? Yes.
10. Are homicide detectives distinct from other detectives? Training? Pay?Not in my department, but in some places they might be.
11. Are there names for other types of detectives? B&E specialists, maybe? Sex crime specialists? Organized crime specialists? Yes. We have Crimes Against Persons, Crimes Against Property, Auto Crimes, and Arson where I am.
12. Do detectives wear their own clothes? We do here.
13. If so, is there a standard level/style of clothing? During "Work Hours" we are required to wear a shirt and tie. When we get called out after hours to work a scene, we can pretty much wear what we want as long as it isn't shorts. (I usually wear blue jeans and a department T-Shirt.)
14. Do they have a clothing allowance, maybe? We don't, but I know of a department nearby that does.