binding safely: pls pls take it off if it hurts after less than a couple hours and size up!
you should only be wearing for under 8hrs i think and wearing it for longer can seriously hurt your ribs. i messed mine up so bad i cant bind anymore. seriously, it isnt worth it to bind more than you can/
for putting it on correctly, you want to make sure that your *ahem* misplaced balls *ahem* arent laying flat, try and mimic where thin or fit amab's nipples are (slightly to the sides & center of the rest of the chest) for the best comfort and most realism.
don't expect for binding to erase your chest entirely, they are meant to make it smaller but also give a more masculine appearance. if you look at cis dudes their boobs / ribs tend to stick out a bit from the rest of their body. i guess what im saying is dont have unrealistic expectations.
hiding binder: i had to do this for awhile too, no shame in it!
first off it helps if you wear 'shapewear' tanks on a regular basis as well, or just any stretchy tank undershirt. they look very similar to binders & if you have a couple you don't even need to hide your binder since it will blend in with the rest. also it is super comfy on its own & if you have a problem with tags in shirts like i do it blocks them out completely and feels like a second skin.
otherwise unusual placement helps! like if you have a stuffed animal with a velcro or zipper back you can take out some stuffing as a little pocket for your binder when you aren't using it.
my parents r nosy and would look through places like sock drawer, under cabinets, under/in mattress, in baskets/drawers, and back of closet on a regular basis and never found it. plain sight works best.
also neo's idea would be good! say you want to cosplay or dress as a male charecter and have it for realism! then if you have a bag for the costume you can keep it in there when you arent using it.
as for making it so they dont notice you have it on, it helps to pack it when you go somewhere they wont see you (like school) in your bag (maybe in a period pack / with pads & tampons) and then go to the bathroom and change when you get there.
if you do meet them per chance, depending on ur size sticking your chest out or having better posture than you usually do can save you. otherwise if you have a jacket you can put it on and button the first couple buttons leaving some underboob to hide the fact that its smaller than it was before. Or just crossing your arms / resting your upper body on something like a table can help.