Hi G. T,
At 13 (at least on American Airlines) the parents have the OPTION of paying the unaccompanied minor fee - which is required for kids age 5 - 12 who fly without an adult aged 18+, but optional for kids 13-17.
As far as 'helping' - they will provide the level of assistance they would provide for any other traveler - but I wouldn't expect them to go above and beyond without you paying the unaccompanied minor fee.... we pay that so the airlines will ENSURE that my daughter gets from point A to point B safely and without chaos. If you aren't paying the fee, you may encounter some "bumps" until your grand daughter gets comfortable.... but I would think that would depend on the airline employee you encounter. I've heard there are some out there that are actually nice and helpful without being told to be that way!!!!!!
I don't know about all airlines - we chose for my daughter to fly American Airlines only (for a variety of reasons). Their unaccompanied minor fee is $100 EACH WAY.
I would think - but I don't know, you'll have to check - that even if you aren't paying the unaccompanied minor fee you would still be able to get a "fake" boarding pass and walk with your her through security and wait with her at the gate until she boards - you can't go on the plane with her, though. So, she'll have to handle her luggage, find her seat etc on her own.
As far as changing planes - you'll have to ask if they will help her (again, they will help her as far as they would help any other adult who asked questions) without you paying the fee. When you pay the fee there is an agent who is ASSIGNED to stay with her until she gets on the new plane to the correct destination.
I don't know your granddaughter - I am happy to pay the $200 (well, OK we split it so it's 100 from me and 100 from her dad) even though I can't really afford it because it gives me HUGE peace of mind that she will have a bad experience (best case) or end up in Toledo (no offense Ohioans) instead of Chicago.
Good luck.