This sentence could come in handy if you needed to remind a friend with amnesia who you were... or if you were writing a soap opera.
tu = your; tú = you. "Soy tu amigo" = "I am your friend"; "Soy tú amigo" = "I am you, friend". That second one would be an odd thing to say :)
Could saying Yo estoy tu amigo be like saying I will always be your friend, or I am a very good friend, ie I am loyal
You could but it's not common, «te hablo luego» (talk to you later) or «nos vemos» (see ya) are more common.
"Yo soy tu amigo." instead of this can we also use "Yo soy usted amigo" ?
No because "tu" means your and "usted" means you. You might be confusing "tu" with "tú", in which the latter means "you" and the former means "your".
Why "Pay attention to the accents" I cannot see any, when everything else is correct. Do you get that if you miss a full stop?
It shouldn't happen if you miss punctuation of any kind. Maybe you fell into a habit and wrote tú? Else I'd recommend just to ignore it. :)