most Micro USB chargers will charge any micro USB device. its a universal standard.

depending on the power rating it will just charger slighter slower or slightly faster. dont get hung up on the details.

just use it

 

It should charge with the phone off or idle. 350ma may not be enough to charge while actually using the phone (for instance watching video, it will lose ground). A USB port should be able to supply 500ma and that will charge slowly while idle. Ideally you want 800 or more, from an AC wall wart type charger for best charge times and/or charging while in actual use.