Brain freeze today!

[Illini_Ref]

FED rules.

For whatever reason, I am having a brain cramp and second-guessing myself on a subject that should be simple.

1. Two outs, runner on first. Batter hits a HR over the LF fence. Batter-runner misses second and is out upon proper appeal. One run scores. Correct???

2. Same thing but the runner that was on first misses third and is out upon proper appeal. No runs score. Correct???

3. Same thing, but batter-runner misses first and is out upon proper appeal. No runs score. Correct???

What brought this up was this. My son is a senior and I have went "inactive" with my umpiring license in IL to watch him play. His team was playing Saturday and I was standing along the fence on the first base side just past first base. The batter hits a HR and I watched him miss second by a foot. He even stutter stepped and I thought he was going to go back and touch, but he didn't. After he touched third and headed home, I got out coach's attention and told him that he missed second. We appealed and the BU ruled safe. After the inning, the BU whom I know, came over and asked me if he missed the base. I said "by about a foot". He told me that he had assumed he would touch the bases and that he wasn't watching. Luckily it had no bearing in the outcome.