4: no answer is required there, saying " Introductions all round" is perfect 6: The sentence itself sound illogical , Would be better " Your mom will remember me, she is a nice person" 7: for ages or in ages, both are fine 9: how are things for you 10: I am very busy with work.... and i've got my cousin staying with me 11: no correction needed for this sentence feel free to send message if you like to talk more or ask questions :)

5/ ON further acquaintance 9/ WITH you 10/ WITH work or AT work actually depending whether you mean the workload or workplace. 11/ no preposition ….,something slips your mind = you forget 12/ to take someone FOR someone else….to mistake someone for someone else.