You'll actually get more of a noticeable benefit turning it on earlier in cases when you might need to preserve as much battery as you can if you can foresee that for a particular day or time period.
If they appear on the lock screen and thus turn the screen on perhaps often then it can add to the battery usage from the point of view of the screen being on more often (and sound/vibration coming on perhaps). Otherwise, not really much of a noticeable impact.
difficult to say. If you have background app refresh on (which you won't if you have low power mode, but anyway...) then notifications - both visible on lock screen and silent, invisible ones - can initiate background refreshes which can use more battery. and as C DM notes, any notifications that wake the screen will use a bit more battery too in powering the screen
It turns it down by around 1/3 of its power or so. If you are mostly doing things like calling, messaging, email, safari, and a few apps that aren't heavy (like some social networking or sports or weather or the like) you likely won't notice any difference.
I'm sure that is the case, however, I can only guess "low power mode" is equivalent to "power saving" on windows and locks the cpu speed to some arbitrary low number (plus other things). You can feel it as the phone feels a bit sluggish.
It could work like Intel Turbo Boost, instead of boosting the frequency keep it the same but just down lock for low level tasks.
Bluetooth is low power and shouldn't be draining the battery much. Many people don't have bad battery life. What do you typically get as your usage and standby times by the time you are basically out of power?
I find that I get more out of it enabling it before. It still provides savings at 20% of course, but they are more noticeable if enabled before.
