Happy to report that the second session went as well as the first. My son needed a bit of reminding how some of the rules worked , and what each party member is best at doing, but he is starting to get it.
*please note that while many names and themes I mention may seem cliche to us, myself included, this is ALL new to my boy and he is enjoying the hell out of it.
Some highlights of the second (much longer) session:
The Illusory Black Dragon (a Kobold) was taken out after Regdar went down from it's Acid spray. After gathering their wits, and joyful of Redgar surviving the party moved further into the ruins of the Alchemist's Lab, finding some trinkets and a tough fight with some Skeletons ensued.
HERE is where I noticed a major problem with the Black Box set. THERE ARE NO RULES FOR CLERICS TURNING UNDEAD. AS I had described this ability in my re-iteration of roles at the strat of the session, my son wanted to use it- nothing on the character sheet, nothing on the rulebook- I was a bit iffy on details as I had not run 3.x since 2003-ish and no longer owned the rulebooks. I grabbed my copy of the Pathfinder core rules, and proceeded to make a quick ruling using channeling positive energy. My son however likes Eberk to get into the fray, and quickly changed his mind, which was a good idea, as the DR of the Skeletons were giving Redgar and Lidda fits. The warhammer showed it's value as boney arms, legs, and heads were taken off. Eberk was down to one hit point, no healing was available/left, and the party decided to head back to the town of Gildenrift (a name that popped into my head when my son asked - its from the 2.0 Core Rules CD intro movie) instead of risking a nights rest in the Dungeon.
Having returned the Barron's stolen ring previously, the party was enjoying a free weeks stay at the Green Griffin Inn, and after some rest headed off to the local trading post to sell some of the trinkets. Some roleplay ensued here as he haggled over the price of some fine bowls/dishes, and he was advised to visit the town mage in his tower at the edge of town to go about indentifying/selling the alchemical powders and liquids they found. Again a name just blurted out, and off the party went to seek out Elminster (gah!!!). A few more gold coins were had, and back off to the ruined lab up in the hills they went.
A wandering pair of Orcs caught the party off guard in a previously cleared room, and a hellatious fight ensued with plenty of extremely high, and extremely low dice rolling on my part as well as my sons. Eberk again went down to one HP, and Regdar, trying to save the Dwarf, risked limb and life taking an AOO to put himself into a better position to protect his friend. Regdar was pummeled twice by stout Falchion blades,and himself nearly killed, but with a mighty swing of his Greatsword, backed up by a Magic Missle from Aramil, the Orcs went down.
After a bathroom break for us kids, and the casting of a Cure Light Wounds, and the reading of a scroll of the same, the party explored it's way into a muchroom/spore cavern. Again wisdom did not win over with my son and Lidda immediately went over to search the sole blue colored spoor patch which loosed it's poisonous surprise. Fortunately the saving throw roll was high and the party retreated to the last room, and off in the opposite direction.
After taking several minutes and making lots of noise to bust down a stuck door, Lidda used her move silently to cross a large open area by herself and listen at one of two sets of double doors in this new room. The sound of the other double doors slamming open against the wall, and the shrieking yips of 4 Kobolds (a tough sound effect to make!) running out to slaughter the halfling made my son jump again in his seat.
At this point again, I called it a session despite desperate pleas to continue
We discussed the session, I gave him some pointers, and he gloated/bragged about a couple of battles where he "PWNED" the Orcs and Skeletons.

I reminded him of how poorly he had rolled at times, and he better hope his luck turns around! He agreed that the randomness of the dice did make the game exciting, even when he was really worried about the consequences of a poor roll.
Though the gameplay/adventure has been very basic/cliche, I'm having far more fun running such a game with my boy, than I do a "full fledged" game with Adults

It's a blast to get back to the roots of the game, and play adventures very similar in scope to the adventures I first played in back in 1977/78.