Basement – How to install fire blocking while finishing a basement

Rather than go to the trouble and expense of tying external insulation from below ground to the siding, I'd let them stop with the below ground insulation. It at least will add a little extra R value.

Then, since your basement is unfinished, but you do use it, I'd go ahead and add additional insulation on the inside of the house* - from the ceiling on down, at least to several feet below the external ground level if not all the way down. (Those extra few feet won't do much on the bottom but they will help some and they won't cost much more...)

*Making sure that any other potential water issues have been dealt with

The key thing with insulation is to get a continuous thermal break. Even a small gap in the insulation can allow huge amounts of energy loss, and since you are running heat downstairs, while I don't know precisely how to calculate the long term savings, there will be one, and more importantly, your basement will be much more comfortable for year round use.

I'm not aware of anything special for fire rating a joint in drywall, just use the same joint compound and tape you would use on the rest of your walls. Fire rated drywall will cut similar to normal drywall, but it will offer a lot more resistance because of the embedded fiberglass.

When sealing any gaps or cracks, they make special fire rated expanding foam and caulk. They tend to be orange in color. There's also fire rated insulation that can be used for any utility chases/bulkheads that connect to the ceiling.

For junction boxes, we've been required to box our in on common walls (2x4 above and below the junction and a piece of plywood behind everything) to ensure that any shorts in the electrical couldn't travel to another unit, but I doubt this would be a requirement for anyone in a single family home.