This is depressing that we have newcomers already scared poopless of bricking their watches.
To the OP, you're fine to install the FW at anytime. The majority of pebble is idiot proof. You don't need to worry about breaking it. Feel free to shut it down and generally play with it. Your chances of having an issue are relatively low.
If you run into a problem there are two things you can do to reset it: 1) hold the center button down until the watch resets. This is good for frozen screens etc and will fix most of your issues. And 2) hold down the center, up and back buttons until the watch enters recovery mode; this will take a good 30 secs.
Once you've become more accustomed to the watch and the forum, the pebbledev.org wiki page, etc you can make your own decisions about what firmware to run, whether you want to turn it off or not.
Another thing to consider is a screen protector and/or body skin to protect the watch from scratches.
Regarding the charging you should be seeing a battery icon in the upper right hand corner when the charger is connected. But not while displaying a watchface. Also if i recall correctly, 1.5.2 may not display it. So no worries there if it's not showing up.
Again your best bet is to update to 1.9.0 using the android app, and just go from there. Let us know how you get on.