Well. I understand that it's really confusing because we use two different words which are equivalent to one in English. Я иду на пляж - it means that I am going to the beach by foot But if Я еду на пляж- I am going to the beach by bus, car or train. Please, pay attention that I use present continious here. Я хожу на пляж- means that I usually go to the beach every day or every week. In short I do it regulary. Я часто езжу на пляж на машинею mtans that I go to the beach quite often by car. I hope it helps. If you have any additional questions, please don't hesitate.

Truth be told Nobody knows :)

There are not any difference absolutely. You can use any variants. it will be correct in any case.

http://www.russianlessons.net/grammar/verbs_motion.php

Could you, please, give an example? What makes you confused? идти или ходить?