Not exactly. You must take out of the verb its ending ('ют'), than add the suffix ('ющ'). In general, there are 7 suffixes of participles. Shall I give them here?
Yes " Я встречаю Пушкина" , but 'Я встречаюсь с Пушкиным' 'ым' - is the ending of noun. It depends on case, declension, gender(he, she, it), number(sing., plural).