A terrapin without a basking spot is likley to be an shell rotted, skin lesioned, respitory infected and eventaully dead terrapin after a while. In the short run it will be okay but get a basking spot asap.
This lack could definitely be contrinuting to the problems you are having.
Ironically the sunshine is better than any basking light both for overall health and for dealing with the skin/shell problems.
So that's good but make sure its not too cold or to hot where you put the turtle.
As for the green in the tank...i would take the opportunity to completely brake down the tank. Clean filter parts (throw away media and replace with new) clean tank and decor and substrate with a bleach solution and then rinse and rinse and rinse and rinse....
This is usually the only way to eliminate algae permenantly in a small tank.
Once you have a basking spot and the water is clean try dry docking her over-night. Just rinse the turtle in warm water and then put her in an esacpe-proof but not closed (well ventiliated, no top is usually best) plastic box overnight and rinse and return her to tank in the morning. Sometimes a week of this will solve all problems if there are also adequate basking facilities.
If not you may need to get some antiseptic (Nolvasan or a generic form of chlorhexidine gluconate or chlorhexidine diacetate is best) and apply that prior to the dry doicking.
Try to do partial water changes every week rather than total ones every two weeks.
Also, you said this turtle is 6 inches, but was that the size you got it? Is it from a pet store ? the wild? (no judgements here). I just want to know as terrapins that were living in the wild sometimes are hard to acclimate to fresh water.
Also its a good idea to get a dechlorinator for your tap water from a pet or aquarium store.
Do you know the pH or hardness of your tap water?