Americans Confuse us a lot

Growing up, during my elementary days we were thought the alphabets. My teacher thought me that the letter 'T' is pronounced as 'Ttsee' if you know what I mean. She also said that 'R' is pronounced as 'arrr'. I was very happy with that until I grew up and started conversing with people of other nationalities. One of such people that have succeeded in planting doubts or confusion as it were in my mind as to what the correct pronunciation is  are Americans. When they call water- Warrer and Peter Perrer I get confused. Since we as a people are all about learning and adopting western lifestyles and basically everything west, should I continue to pronounce T as Tsee or Ree? and most importantly how do I teach that to my little girl who is just starting to learn ABCD?

Again here's letting you into my loud random thoughts
Chioma Azosiri
08:58 AM 16-07-2016