Friend bought a Chevy blazer2006 from a guy it had been sitting long time and he said fuel pump was going out. It hAd trouble holding pressure. Now that it got cold at night can't get it to start would fuel pump go out just like that? And my brand new battery looses charge now too?
Fuel pumps most commonly fail due to worn brushes that don't make good contact. They either make contact or they don't, so yes, they do go out just like that. Typically though, Chrysler pumps almost always fail to start up, leaving you sitting in your driveway. GM pumps have a reputation of failing while you're driving, leaving you sitting on the side of the highway.
There are a number of other things to look at for the symptoms you described. For not holding fuel pressure, the most common cause is a leaking fuel injector but you also have to look at the pump and the fuel pressure regulator. None of those will cause a failure to start but they will cause a long crank time. You may overcome that by cycling the ignition switch to "run", waiting a few seconds, then turning it off and back to "run" a second time, then cranking the engine. That will give the pump twice as long to run for one or two seconds to build up pressure.
GM has a big problem with their generators. Due to their design they develop huge voltage spikes that can damage the internal diodes and voltage regulator, and can interfere with computer sensor signals. When one diode fails, you will lose exactly two thirds of its current-generating capacity. 30 amps from the common 90 amp generator is not enough to run the entire electrical system under all conditions. The battery will have to make up the difference until it slowly runs down over hours or days. Due to the numerous unnecessary computers, it IS more common now to have a drain on the battery, but before you get involved in a difficult and expensive diagnosis that may not be needed, have the charging system tested with a professional load tester. The important numbers are full-load output current and "ripple" voltage.