I can do this. 나는 이것을 "할 수 있습니다." You may do this. 너는 이것을 "해도 됩니다." You can/may smoke here. 당신은 여기서 담배를 피울 수 있습니다. 당신은 여기서 담배를 피워도 됩니다.

You should listen to TTMIK lessons. Can has at least two meanings in English. ㄹ/을 수 있다 and -ㄹ/을 수 없다 - used when expressing or asking for capability. Can you cook food? http://www.talktomeinkorean.com/lessons/level-2-lesson-17/ May/can -도 되다 - permission. Can i eat this? http://www.talktomeinkorean.com/lessons/level-4-lesson-8/ as for your other questions.. listen to all the lessons. they have a lesson on should/shouldn't.