Yes you can cast spells on other people and do workings on them. Whether or not you ask their permission before hand is up to you and your ethics and morals. As general advice before doing any working involving someone other than yourself, just think about how it will affect them before you considering affecting them and their life in anyway. Think about the consequence too and other people it may affect. But ultimately it is up to you to decide, but as said before you do not technically need a persons' permission, however I personally ask out of respect.
As I said before think about the effects the spell will have either on a person, yourself, or multiple people. Magic is manifesting your will into reality among many other things and in all sense any action has an equal and opposite reaction. I usually tend to think heavily and contemplate on any spell and working before I actually take action and proceed with it. However the most important thing is to focus, be specific on your goals and intent, and then use your desire and will to cast (manifest) it into reality.
As far as your question about liking a anime/manga and wanting to be in a artificial world that simulates it, my best suggestions for your are Lucid Dreaming and Astral Projection, as well as Creative Visualization. Each of those methods have the ability to simulate or project your will and imagination into almost anything you wish, although to create such a detailed world as you'd like would most likely take many years and patience to practice and experiment with different techniques. But other than that there is no way to actually transport yourself to an artificial world in any sense of the word.
I wish you luck in whatever direction and path you take. I also encourage you to read, study, and practice the basics as you are just beginning on your magical journey.