どう (dou) does mean how, やる (yaru) is another word for "to do." どうやって (dou yatte, not douyade) is how to do, so the proper way to ask would be どうやって東京に行けばいいですか。 (dou yatte toukyou ni ikeba ii desu ka?) the meaning of this would be "how would I get to tokyo?" using ikeba ii in this case is more like "how should I go about doing ____" using ikimasu in that sentence is more like "how do you go to tokyo?" and isn't exactly asking for help (although most people would catch your meaning from the lost look on your face).
I found one of the easiest ways to ask for help is to say what you want to do. by saying すみません、東京に行きたいんですけど。。。(sumimas en, toukyou ni ikitain desu kedo...) usually the person you ask will take it from there and give you help. If they don't catch on, you can through in どうやって行けばいいですか。 (douyatte ikeba ii desu ka) to make it explicit that you are asking for help.
the "shashin" sentence's grammar is "is it alright for me to do something," and it should be "shashin wo totte mo ii desu ka" (in more casual situations, particles like "mo" are sometimes dropped, but to be proper I would leave it in) Totte (the "te" form of toru) is indeed to take something, and it could mean to grab something as well as to take a photo, but the kanji are different.
something in the "te" form with kudasai or onegaishimasu is please do something (like something wo shite kudasai), it's a polite way to ask someone to perform an action for you. mou ichido is one more time, itte kudasai in this case means "please say." you could also say "motto yukkuri hanashite kudasai," which is like "could you please speak slower"
all of your questions seem to revolve around the te form, I would recommend studying it a bit, as it is very useful and has many applications.