How long does a fully charged battery go? Might buy if good.

Same as any other quarts watch and either way a new battery costs $5. It's the best $40 I've spent on anything.....maybe ever. I've owned it 5 months but even if it broke after a year it only cost me 11 cents a day to wear what looks just like a Rolex and keeps accurate time.

Can you take the links out to make it smaller?

Yes, you can use the watch band remove tool to remove the links, if you dont have these tools, only one Hammer and one Punch Pins is ok.

Does it tick or rolls?

IT TICKS ....... ROLLS IS A PERPUTUAL MOVEMENT

What is the smallest size in inches

I'm not sure what measurement you want, but the body of the watch is 1 and 13/16 inches wide and the band has a 10 point adjustment that can go all the way down to a very small wrist. They even send you a little pointed tool for adjusting the wrist band size. This is the best value in watches, that I have found. I bought all 3 colors; blue, black and green. I get compliments on all of them.