Being telescopic, it will take either 18350, 18500 or 18650 batteries.
18350 are the smallest and 18650 are the biggest. These can be purchased in several different vendors. Now the difference in Batteries, is the 18350 are better for out and about, but the 18650 will last a damn site longer, so I would look for a couple of each, with the 18650 being of high drain
As for a Lanyard, I am pretty sure you wont get one, for a mod of this size or weight
If you mean mAh, then no, what it does mean is the higher the number, the longer it should last between charges. I would advise that you contact Coolvape, as some of the bigger 18650's might not fit or work in this model.
Also, as its a Variable Voltage (Can adjust the voltage) I would also look in the manual to see if it has circuit protection. If it does, get the 'flat top' batteries, if it doesnt get the 'nipple top' batteries