Is there any chance to charge battery outside the phone without using external charger and different phone? My Nokia N900 is not booting for some reason. So I must reflash it, but it is impossible without charged battery. My battery ran completely flat. Please help.

Ehm... how do you want to charge battery outside of phone without external charger? You can charge it either in phone (with charger) or outside of phone with (external) charger. Without charger (of some type) it is obviosly impossible.

And for these caches I have external charger Nokia DT-33.
http://download-fds.webapps.microsof...-33_QSG_en.pdf

Or someone can send/lend you a fully charged battery

When I turn my N900 on with battery inside, NOKIA logo is shown on the screen and red LED is always on (not flashing like during normal charging). What does it mean? Maybe battery is charging, but in different way?

Nokia N900 can charge battery without OS to level at which it can boot NOLO and linux kernel (for starting BME needed for charging). But that level is not enough for entering flashing mode in NOLO.

Can I use rescueOS to charge battery without entering flashing mode?

No. Without charged battery you can boot only and only system in NAND.

pali is right, you need a charger of some sort. It could be anything that uses the same kind of battery. Other phones, not just N900 (old "dumb" phones are the best), or other devices. I once had a Bluetooth GPS receiver using the same battery that could be charged from a USB port.

Your best bet though is to invest in a universal one, like e.g. this one (in your country variant, obviously). It costs peanuts and can be used for anything: cameras, other phones... Ever since I got mine I am not taking anything else on holidays.

I wonder if voltage can be different from nominal 3.7 V (for BL-5J). And how connect my battery with the other charger (or phone).