If my opponent has multiple untapped characters when I use Blurr’s ability, which one does it attack?

You choose, just as you would for any battle.

Can I play any cards in before it attacks the untapped character?

No. The second attack starts right after the first one finishes.

Do I have to attack a second time, or can I just leave Blurr untapped?

You do. Note that if there isn’t an untapped enemy, the ability doesn’t trigger and Blurr won’t untap.

If I have a Grenade Launcher on Blurr, and I attack a tapped character, which will occur first: the second attack on an untapped character, or scrapping the Grenade Launcher?

Grenade Launcher only lasts for one battle, so it would be scrapped before Blurr launches his second attack.

Does Blurr’s ability combine with Mining Pick to allow you to plan 2 again on the attack of the untapped character to get +5?

Yes.

How does brave interact with Blurr? Let’s say an opponent taps their first character which has brave. I attack with Blurr and he lands attack damage on the tapped brave character. Is Blurr able to still attack an untapped opponent or does he have to/is he able to attack the brave opponent?

Blurr must attack an untapped character and thus is unable to attack a tapped character with brave. If your opponent also had an untapped character with brave, Blurr would have to attack that character.

If Blurr attacks and deals damage thus triggering his effect, if the only untapped character(s) left have stealth, will Blurr not untap? Or will it still untap and just not attack again?

Blurr will untap and Blurr will attack one of the characters that has stealth.