My suggestion is to define your goals and figure out what you have to do to reach them. If only reading and writing are your goals, you can definitely learn it on your own. but to practice speaking and listening you really have to talk to another person. That said, there are so many resources out there that you don't really need an actual teacher.

I learned English from watching Simpsons and eventually started talking English to people. It is possible but you really need to speak with people.

following a basic plan of memorizing words ( let's say 30 words per day ) would give you (30 *30 days ) = 900 word per month meaning within 3 months you will have 2700 which is great in addition to that I recommend practicing with a native English speaker.

I think that if you work hard enough, and remain consistent with your lessons, then you could definitely learn English on your own. It never hurts to ask questions though, especially when something may be confusing you :)

Well, you are asking the question, so you are already not learning independently. To answer your question more completely, I would say that you can learn a great deal on your own, but when it comes to speaking and listening it is important to work with other people.