Is my 2yr olds behaviour normal?

My daughter has just turned two and I am having a few aggression problems with her, mainly tantrums. However my questions relate to other things my daughter does, for example, at my grandmothers house she lined up number fridge magnets from 1 to 6 and then my mother mixed them up again moving all the numbers about but she then proceeded to line them up verticalling in order and facing the right direction. She pretend she can read by saying random letters as she points to letters,she can count to 16 though not in a row mainly she counts from 1 to 8 or 7 to 16 but never straight through. She can also sing all the words to "eyes on Fire" a song which features on a twilight album I noticed she knew all the words after i played the song about 4-5 times and says every word clearly. She has a very extensive vocabulary, though her 3 yr old brother has call me deceitful and vindicitive and when asked what vindictive ment he said i was a liar and cheated him all because im told him the wrong time for a birthday party. She knows some colours and knows simple shapes such as triangles squares and circles. she also began to sing row row row your boat which she picked up at play group shes probably herd it 4 or 5 times in her short life and yet she sings it alone in her room along with old macdonald another song i didnt teach her. one day after a vry inding day she decided it was a storm then spent the next day looking and asking people if they had seen a rainbow, also she dosent deal well with new people or places. She also loves to pretend shes a dog and licks me and barks at least 3 or 4 times a day, is all of this normal????