Hi,
Here is a link which shows how to replace the battery. They also supply the battery and opening tools
https://www.youtube.com/watch?v=O_TV-HBCM50
Here is another link where you can purchase the battery.
http://www.amazon.com/Garmin-Nuvi-265W-Battery-Replacement/dp/B00FABV3Z0
As for the mini USB connector, you may have to remove it first to see if there is some securing lug differences to a normal mini USB and then try Ebay where there are plenty of options. Here is a link
http://www.ebay.com/sch/i.html?_from=R40&_trksid=p2053587.m570.l1313.TR1.TRC0.A0.H0.Xmini+USB+female+connector.TRS0&_nkw=mini+USB+female+connector&_sacat=0
Also, for what it is worth, here is the pinout for the Nuvi mini USB port.
http://pinoutsguide.com/GPS/garmin_nuvi_power_pinout.shtml
Hopefully this is of some help.