Where can I see my current search ads $$$ balance? I've entered the promo code, but can't find if it's done successfully. And if I want to add some of my money? How can I do that?
Current Balance
If you go to the Search Ads page, then click on your user name in the top right (note: this only appears for me on desktop, NOT mobile for some reason), then Settings and finally on Payment Info you can see all your credit card transactions at the bottom. These should also get emailed out to you.
Note that you can't actually see a balance here, so your free $100 credit doesn't actually show up. If you look directly under your credit card you should see a line with what looks like a UUID, followed by Expires 12/31/2016. This will at least let you know they've applied the free credit to your account.
To see when it finally runs out, you're going to have to work that out yourself by looking at each of the invoices at the bottom. You sort of have to trust that Apple have applied it correctly as far as I can see, and just check once it runs out by when that happens on your invoices, or if you're like me, you'll probably reach the credit expiry at the end of December without having spent all of it. I jest slightly, i've finally got it to a weekly run rate where it looks like that will run out before then.
You don't have to add more money manually - Apple will periodically raise one of these invoices and bill your card. If you're not spending very much you'll probably only see one of these each week. They should only start billing you for a non-zero amount once the initial free credit runs out. I think because the initial credit is a bit different from normal operations, that's why you can't see a balance anywhere - they didn't consider this mode of operation when building the site - they were expecting just to invoice you and bill your card.
If you want to see what you've spent since the last invoice, as far as I can tell you'll need to work that out from the front page, by setting an appropriate date range, and adding the amounts in the Spend column. It would be nice if Apple gave us total columns here, as the absense of them on the front page is a bit strange on what's supposed to be like a summary dashboard.