I worked at an electronics store for 3 years and have tons of experience with autostarts and alarms. Ill try and clear up a few things.
#1 yes your keyless will still work with your stock remote but i would recommend using the autostart remote only the reason is some autostarts (specifically ones with a single lock/unlock button) only know how to do the opposite of the last function. for example if you lock the car with your autostart and then unlock it with the stock remote and then try and use the autostart to lock it, it will first unlock the car. its confusing i know but just trust me
#2 yes you immobilizer and stock securtity will need to be bypassed but that doesnt mean they wont work. they will still function just like stock except for when you autostart the car thats the only time the modules used to bypass those systems are active. So, you dont lose the protection of the immobilizer key and your stock alarm will still function.
#3 If your worried about leaving your car running unattended, dont. As soon as you put your foot on the brake to shift out of park(unless the key is in the ignition) the car will turn off. So, if you have nothing of value in the car you could basically leave it unlocked your car isnt going anywhere. (with out your keys)
#4 I strongly recommend buying one from a reputable dealer and having them install it. Here is why, They are very complicated, Most reputalbe brands require for warranty that it was proffesionally installed, i have personally see cars that have started on fire or been cause thousands of dollars worth of damage because of poor install, our cars in specific (7th and 8th gen) are not very easy if your gonna try your first autostart do a chevy truck they are easy as hell. Also Best Buy is not a reputable dealer (At least around here). They cannot use solder because of insurance reasons this makes for a poor install, Im not saying this is true everywhere but In Fargo ND where im from the installers there are Terrible, i wouldnt send my worst enemy there.
#5 this is just my opinion because of my experiences. Brands i have had good luck with quality wise are Compustar, Astrostart, and any DEI brand cause they are all the same anyway with a different sticker. Some brands are better at different things so if you know what you want it to do but not what brand and model to get just let me know i will help you pick one out.
I hope this helps and feel free to ask ?s cause im sure i missed a few things