1st all grain..have questions

So I'll be starting my first all grain batch as soon as my grains arrive, but i have a question or two for those who know....
I built my mash tun today from a 48 qt coleman cooler, i used the braid method as it was the cheapest and easiest to start with...tested for leaks and all good.
I have a 32 qt pot for full boils when the weather gets better, but I'll be brewing indoors on my stove (ceramic top) for the next month or two. The problem being that I cant get a full 5 gallon batch to a boil on my stove....but I have a smaller 5 gallon pot that I can do 2 split boils in.
My question is, can I do that? Can I mash my full grain bill, sparge, and then boil half while the other half of the wort sits off to the side. When the first half is done cooling, can I then continue with the last half, cool it and then add to the first in fermenter?
Is there a problem with half the wort waiting an hour or more before boiling?
Oh ya, I'll be doing Ed Wort's Haus Pale ale...seemed like a great starting point for my first all grain.

 

I would use two pots to boil (the 32 qt and 5 gal you mentioned). I did this with that same beer and turned out fine. Just do your best to split the first runnings and the sparge between the two pots and then split your hops additions and you will be fine. I am limited by pots and stove output so this is my standard operating procedure and it works fine. One pot will always boil first so just make sure keep track of boil time for the two different pots...

 

No garage unfortunately, I'm limited to the stove until its warm enough to stand outside for a few hours.
As long as it isn't hurting the wort to sit for a while before boiling, I don't mind a long brew day. I'm a chef by trade, so a whole day in the kitchen is how i usually spend my Saturday anyways.