I was a first time GM when I started Rise of the Runelords too :) And now my group is only a few sessions away from the end of the campaign!
Definitely make use of the threads here on the forums; there is plenty of useful stuff, especially for the early chapters. Also do try to at least skim the chapter summaries of all six chapters to have an idea of where things are going.
For general advice, I'd say you don't need the bestiaries - even though I have them I just go to one of the online resources and print out the monsters I need for a session - allows me to make notes and whatnot.
I followed the book quite closely early on, but my group soon became more powerful than the encounters as written, so don't be afraid to deviate from the book - this will become easier as you get more comfortable GMing. I changed a huge section in the middle of the campaign to better line up with the actions of the PCs! As el cuervo said above, there's no right way to run a game. As long as everyone is having fun, you're doing well :)
If you have more specific questions, feel free to ask! :)
I generally choose to give a challenge when the battle is not really significant - just normal mobs/random encounters. I have still killed PCs this way due to their casual approach to tactics. Bosses and significant battles are a lot tougher and have a higher chance of killing PCs - but that is usually when they step up and actually plan their tactics etc!
It certainly sounds like it might be worth chatting to the GM. S/he may simply have forgotten/not thought about the aspects of the rules that you mention.
I know I rarely bother with Handle Animal checks for animal companions as I assume the ranger/druid knows how to deal with his own pet. However, if said ranger/druid hadn't bothered to actually put any skill ranks into Handle Animal, I would probably make the pet do unexpected things.
Not adjusting CR or loot may be an experience thing. I certainly shied away from that when I was just starting out. I now try adjust encounters to suit the group, though I often end up making things a *tad* too difficult (generally resulting in at least one death)... still, I wouldn't have learned anything if I'd never tried ;)
My players have died a few times over the last while...
Name of PC: Cecil
After leaving an enemy for dead, she alerted Jorgenfist to the heroes' presence, and they walked straight into an ambush... One 4x crit later, Cecil bit the dust.
Name of PC: Nu
After taking a quick detour to Magnimar to resurrect Cecil, the heroes attempted to infiltrate Jorgenfist again. Needless to say, the enemy was ready and waiting...
Name of PC: Cecil
Cecil snuck into a hill giant camp and found himself overwhelmed and separated from his allies. Fortunately there was a druid on hand to reincarnate him... as an orc...
Name of PC: Ciaran
The party went into the black tower last, where they encountered the Black Monk and two of his harpies. All the heroes failed their Will saves against the harpies' song, leaving them helpless for a couple of rounds while the Black Monk summoned a bunch of swarms. Ciaran was forced to use a fireball in the confined space of the tomb, but as he and the swarms were the only ones lacking evasion, he took a lot of damage (fortunately he also killed the swarms). While the melee characters focused their attacks on the harpies, the Black Monk moved in and took down Ciaran in one round...
I've been GMing Rise of the Runelords for a while now (the characters are 11th level) and I've just been using the advancement guide at the start of each chapter to decide when the characters need to level up. Sometimes it feels like they haven't done enough to realistically level up, so I will throw in a side quest or simply delay levelling until it feels 'right'. Some of my players also have an uncanny sense of when they should be levelling, so I use that as a guide as well.