1. He is my friend.

2. He is my male friend.
3. He is my boyfriend.
[ A man is telling a person this sentences. In this case, which one is commonly used? If a man say #3, what connotation does it have?]

4. She is my friend.
5. She is my female friend.
6. She is my girlfriend.
[ A woman is telling a person this sentences. In this case, which one is commonly used? If a woman say #3, what connotation does it have?]

1 and 4 would be most commonly used. If the friend is female, it's not necessary to state that "she" is my "female" friend. "She" is not likely to be a male friend. The same if "he" is a "male" friend. To use "boyfriend" or "girlfriend" might imply a romantic relationship, which is okay if that's what you mean to say. If not, then maybe those words should be avoided.

In general, the commonly used phrases to describe relationships are as follows:

For a man:
1. "He is my friend" - This implies a platonic relationship without any romantic involvement.
2. "He is my male friend" - This emphasizes the gender of the friend, but still implies a purely platonic relationship.
3. "He is my boyfriend" - This indicates a romantic relationship and typically implies a level of commitment, exclusivity, and potential future plans together.

If a man says "#3," referring to the other person as "he" and using the term "boyfriend," it generally denotes a romantic relationship with the person he is speaking to. It suggests that the man and the other person are involved in a romantic partnership, and they may have deeper emotional connections, commitment, and affection towards each other.

For a woman:
4. "She is my friend" - This implies a platonic relationship without any romantic involvement.
5. "She is my female friend" - This emphasizes the gender of the friend, but still implies a purely platonic relationship.
6. "She is my girlfriend" - This indicates a romantic relationship and typically implies a level of commitment, exclusivity, and potential future plans together.

If a woman says "#3," referring to the other person as "she" and using the term "girlfriend," it generally denotes a romantic relationship with the person she is speaking to. It suggests that the woman and the other person are involved in a romantic partnership, and they may have deeper emotional connections, commitment, and affection towards each other.

However, it is important to note that the connotations and implications of these terms can vary depending on the cultural context, personal preferences, and the specific dynamics of the relationship. It's always best to consider the context and the individuals involved when interpreting these phrases.