[AT&T Samsung Galaxy Note I717] CalcProgrammer1:
Battery life isn't the greatest on the Note, but it's acceptable. If you use it a lot, the battery will drain. You can try using a different CPU governor (lulzactive, smartassv2, etc. in custom kernels) to improve battery life or just use powersave (which decreases performance but improves battery life). You also have to account for the huge screen which is OLED, not LCD. With an LCD (like the iPhone 4 has) there is an array of white LED's that illuminate the screen. There's probably 8 or so of them. The LCD glass is a color filter which colors the white light from the backlight. The LCD itself uses little power, and the LED backlight only has 8 or so LED's. The Note uses an AMOLED screen (Active-Matrix Organic LED) in which each individual pixel is four independent LED's (RGBG). They're small LED's and use little power on their own, but you have 1280x800x4 of them (well, not quite due to the pentile arrangement staggering pixels). When they're all on (white screens) it uses a lot of power, especially when brightness is up. On the plus side, when they're all off (dark screens) they use much less power. To save power on an AMOLED, use a darker background/theme.

As for RAM usage, the Note has 1GB and you really don't need to worry about checking it. Android manages RAM very well, especially when it has 1GB to work with. When you leave an app in Android it isn't closed, merely pushed back in an application stack. Only when Android determines that RAM is filling up does it start removing stale apps from this stack.

Personally I've used my Note with many different cables without issue. The included Samsung charger and cable work very well, and I think has the most solid connection of all of them, but I've had success with a cord from my Archos media player as well as my HP TouchPad tablet. The TouchPad's wall charger also gives a slight charging boost as it provides more power (2A vs. 1A) but the Note's highest charge rate is around 1.1A so you don't see a huge difference. It does need a bit more than a standard 500mA USB port provides, so if you plan to charge it off your PC or a 500mA charger, you need to turn off the screen and leave it off, otherwise the screen will eat up the power, leaving none for the battery.

My favorite ROM is CyanogenMod 9. This is a built-from-scratch (Google's source + modifications) ROM that includes a lot of nice features while retaining the stock Android look and feel. I personally do not like TouchWiz or the customizations that Samsung added to their Note ROMs but many people do. It's all about personal preference. A nightly build means that a new release of the ROM is posted (usually by an automated system) every night. This is what CyanogenMod uses for most devices, as their project has many developers and is constantly updating. You don't need to update every day, but a nightly ROM means that you always have access to the latest updates if you want them.

As for the flash counter, I would warranty the phone before flashing a custom ROM. I generally don't take warranty into account on my tech purchases because with all the hacking I do it's often void, but usually if you restore the stock firmware they will fix hardware issues obviously not caused by your ROM flashing..