'Yo alegro por mi' means 'I am happy for me' in English (Google Translator).
Me alegro de que tú eres mi amigo
alegro
Alegro is not a spanish word. Perhaps your confused with the spanish word, Alegre , which means happy.
eres alegro
im glad
If you're a male, you say, "Me alegro que estoy casado." If you're a female, you say, "Me alegro que estoy casada."
It means (I am) glad to see you
"I'm glad you're feeling better" in Spanish is "Me alegro que te sientes mejor". It is pronounced "May ah-LAY-grow kay tay see-EHN-tace may-HORE". Please see the Related link below for confirmation of the translation.____________________________________________________________"Me alegro" is a subjunctive trigger.You're using the verb "sentirse" which means "to feel"So, it should read"Me alegro que te sientas mejor."or"Me alegro que te estés sintiendo mejor."you could even attach the reflexive pronoun to the end of the gerund and say:"Me alegro que estés sintiéndote mejor."(note the added accent on the 3rd vowel from the end.)
Translation: That's good, it makes me happy.
It depends on how you mean "do" in English. If you mean it purely as a placeholder for a different verb, such as the below conversation, you should say, "Me alegro que si" I work very hard at my job. I am glad you do. -- i.e. I am glad you work hard. If you mean it in the sense of performing, i.e. the usual use of "do", then a translation would be: Me alegro que lo hagas.
Me alegro de empezar a trabajar con Usted.