Dry Rot Repair

The front of my home includes a cantilevered section where the living room floor joists extend out 4 feet. Rain water seeped between the cedar, toung & groove and a cedar trim board and caused extensive damage to the ends of the floor joints and beam that caps their ends.

Is there any "treatment" I can use to stop the dry rot process in the sections that are only lightly damaged?

If I "sisted" new joist sections to the old ones, after cutting away the severely rotted sections, will the dry rot continue to spread?

Is there any way to apply a decorative trim board over the top of cedar siding and keep the water from seeping behind the trim? Caulk seems to last only a short time in our wet, Northwest weather.

Any advice is most welcome.

Thanks, Clark