my iphone 5 had msg "no sim card installed" yesterday and today I can not charge my phone.

Yesterday at work I received a message on my iPhone 5 "no Sim card installed". I did a hard reboot and went outside for verizon signal. After a couple of minutes the phone was back to normal. Last night I plugged phone in to be charged it started to charge--around 8pm. Went back to phone at midnoght to unplug and phone was down to nothing. The the lighting plug icon and battery meter was showing and meter is in very low red area. I tried different plugs from my other apple devices and still no luck. Are the two problems related or two separate issues? How can I fix the problem?