I attached a pdf of the scenario i have questions on, please take a quick look at it.
1) Can a service feed be taped without over current protection ahead of the taps as shown in the attached pdf?
2) If the answer is yes, what would be minimum required size for each of the conductors shown in the attached pdf?
1. As long as you follow the tap rules for services and there is an appropriate way and place to make the tap where you want to make it. Another poster suggested a few provisions of the code that might be helpful. You might also want to look at 230.33.
2. It kind of depends on the calculated load to some extent, but if you sized the conductor ampacity to equal or exceed the rating of the CB it connects to it would always be legal.
I think a lot of people are afraid to comment on this kind of question because often a lot of details are left out that might be germane.
For instance, presumably the CT cabinet is for metering and may be owned by the POCO. They may have their own rules about what you can do there.
You seem to be showing a lug or terminal coming into the CT cabinet and another going out. Presumably you would want to tap on the downstream side. If the lug(s) supplied only allow for the three existing connections, it may not be all that easy to get another conductor or set of conductors in there.