I am wondering about american accents -this evening

I have been here for more than 2 years , still i have problems telling people my name... , my p sounds like B to them and my H ..sounds like ..i don't know what.. :) every time i have to spell my  name in a phone conversation to an automated machine, i pull my hairs.To tell you the history... we were taught english back in Nepal, according to British curriculum... so, what's the problem you may ask.. i said the curriculum for english was british, not the teachers ...lol, at best we got Indian teachers or Nepalese themselves , who were taught in turn by teachers like themselves. so when i pronounce my words.. i guess they are mixed of indian-nepali-british accent ... which in itself is amazing, i agree ... but hard for others to understand. so ..i have to repeat in again and again to the automated machine.

And one thing else---- why do people here... swallow their words, feels to me as if they have a Gum in their mouth and they are speaking while they are trying to chew it... , and why do letters in the last or sometimes in the middle do not get pronounced at all... american english is funny, :) and why the hell ...  T in the middle of the word sounds like  a D to me... O, AMERICA....

so i am trying to learn this american accent... and there is a kid who lives next door to me..who is kinda my teacher.. every time i converse with him.. he looks strangely to me, wrinkles his forehead , listens to my words and corrects them.. , it  doesn't last more than 5 minutes though..., tired of correcting , he usually leaves though ... haha .. make me wonder how long will it take me to practise and speak American english   :)

Have similar stories to share? any shortcut to speaking american english faster ? . How did you guys deal with accent of a different country..do share....  :)