Hands are tricky. You could try using plastic gloves, but I'm not sure they'd spread the color well. I usually just put it on the backs as best I could, washed my palms as carefully as possible (so as not to disturb the color on the back), then buffed my hands a little.

As for the streaks and the patch... you could try gently exfoliating the patch - that'll take off some color. I bought some exfoliating gloves so I could carefully go over streaks with just a fingertip. And next time you apply, try to apply around the patch and streaks, if possible. That'll let the other color catch up.

It's probably impossible to avoid every single bit of streaking, but you'll get to where it's close enough to pass for perfect.