On "1. Would the new scout be expected to complete all of the past requirements in order to earn the rank badge?" === > To earn the rank badge, yeah, gotta complete the requirements. Either the handbook ones or the 11/30/16 version, or mix and match as ya like. The 11/30/16 versions will be easier, mostly.
Of course, advancement is just a "method", not a requirement.
He can still be a Cub Scout and just have fun / do activities / get loops.
No need for anxiety here.
On "2. If yes, who's responsibility is it to catch the scout up? the parent? the den leader?" === > Parent.
You signed up for Den Leader to lead the Bear activities once ... your job is not to repeat it every time someone comes through.
You can if you want to, or for part of it.
I mean, sometimes activities you may already be doing (spring camping, hikes, field trips) might easily tie into ways you can help ...
... if you want.
If the Parent is really keen on doing all the "catch up" activities ... they can do them all on their own, on Pack campouts / day events, etc.
But they can also chill out and not stress about it ... have fun, get some loops, have some laughs.
On "3. If he just did the remainder of the requirements that we have left with us, would he be eligible for the Bear Rank Badge?" === > Nope. If he didn't all all Six Required (whichever ones ... recall that the 11/30/16 version made Grin & Bear It an elective (but you can mix and match, it's OK) plus one elective, he didn't "earn the rank".
But he gets all the loops!
On "4. Would it be best for him to just concentrate on earning his Bobcat and then be ready to go as a Weblos I?" === > Nope, but it isn't an "either 'go bust it for bear' or 'just wait fer Webelos'" type of situation here: the best situation would be have him earn Bobcat (easy peasy, really ...) .. and do your Bear activities.
so he gets a Rank Patch for Bobcat,
and let him load up on whatever loops you're doing for the rest of the year ...
... any any other awards you might start that he can finish.
Hope that helps!
