My friend gave me a fairly used LGcu720 shine phone. Its pretty cool but has some problems.when ever I plug the phone to the charger it soon switches off on its own and continues charging but shows the word 'insert battery'.also, I have to disconnect the charger before I can switch on the phone again. And if I plug it in to continue charging while on, the phone will say "charging" but the battery indicator on on the screen might or might not blink. The battery takes long to charge and only last for like 3 hours. Also the screen isn't really all that visible under direct sunlight

Even on my DroidX in perfect working condition, it isn't too easy to see under direct sunlight, I usually have to shadow the screen with a hand or stand with my back to the light. So that sounds normal. The other part sounds like you need a new battery. I would check with a cellphone place that has a nice return policy (make sure there's no restocking fee). Pick up a new battery, try it out, and return it if it doesn't work.

If the new battery doesn't fix it, then you're looking at either dealing with it, or having the phone fixed, which would be pretty expensive.