hey dude, well welcome to the band wagon (finally lol)
in regards to closing apps, since android 2.3.(something) the OS does a pretty good job in managing open apps - i.e. wasn't really a need for task killers any longer (some might say).
other apps are on by default, could be several reasons, try and check out internal app settings to see if anything mentions being left on to run a its service or something (e.g. i have a separate clock widget which will always be running)
but on the 1X? if you click on the recent apps softkey on the bottom on your screen (its the right one along the bottom, the one that looks like a square on top of another), you can close apps by just flicking (the apps you want to close down) upwards.
hmmm...suggestions and tips...
1) utilise the new folder option as much as possible to keep your screens uncluttered (unless you like that sort of thing.
2) having a power widget (one that contains the core switches such as wifi, bluetooth, screen brightness) is always helpful somewhere on your home pages - i use switch pro widget, its costs but ive been using the thing for like over 2 years now from my HTC hero days.
3) be sure to keep your screen brightness to a reasonable level, 30%-40% usually works for me in the office and outdoors (70%-80% if its sunny), saves on more juice due to the screen
4) if you've got a limited data bundle (although ICS now has this) i always install something like 3g watchdog to keep an eye out on data usage. with new smartphones you tend to hammer the data at the start so keep an eye out (unless you have an all you can eat package of course)
5) anything using bluetooth, fast mobile internet (HSDPA+) and GPS kills the battery so try to minimize this throughout the day.
there are more but nothing comes straight to my head
leave the rest of the guys to chip in