Objective 9: Movie Buff. Go to the movie theatre during daytime (not on a date) and ask the guy to get a quiz you'll have to ace.
Objective 16: "Perfect Ending". You will need to raise Mom's suspicion and Little Sis' jealousy to 5, most easily done by Yoga with Big Sis and Mom respectively.
Yes, all cards are around. However, they are tiered and you cannot get tier 2 before you found the corresponding tier 1 pic. Also, some will not be in places but in transport, so try the different options as well. Apart from that they are always in the same place.