I've met so many officials who say that they can't go outside the numbers (btwn numbers and sideline) and there can't be any coaching. I have no idea where this myth came from, but apparently it's the football equivalent of the hands are part of the bat.
Admittedly, the rule book doesn't outright state "here's the type of conference you can have during an injury time out" but it can be pieced together, though again it's a bit of spaghetti code to get there.
From 3-5-8, Authorized Conferences, in subsection 3-5-8 c, we see that only an outside the 9 yd mark conference (between numbers and sideline) can be held in a situation for 3-5-8 a (3). So what does 3-5-8 a (3) deal with? It deals with a time out granted by the official in 3-5-10. So we hop over to 3-5-10. That's the various official's time outs, which right in section 3-5-10 a is the time out for injury.
So not only CAN they take an outside the 9 yd mark conference, it's actually the ONLY type of conference they can take, by rule. I have no idea where the 'no coaching' part came from - we're really going to police what they say? But a lot think it, for whatever reason.
As to the second question, wait till the ball is placed.
Start that baby up as soon as possible.