1. THAT was the first time I HAD met such a tall person (We usually refer to past events with 'that'. 'Had' sounds more natural but either is ok)
This is the first time I HAVE met such a tall person (If you are referring to a current event, aka speaking TO the tall person, 'this' and present perfect is appropriate
2. Because she HAD always been impatient (means: from my past experience talking to her, she was impatient in conversations)
Because she WAS always impatient (means: she was impatient in every situation)
^Either of these is ok
"I didn’t think she was likely to HAVE listened to me for long" --> this means at that past moment in which I am speaking, the conversation I am talking about has ALREADY OCCURED, and I do not know whether or not she listened, so I am guessing. This is probably not what you mean.
"I didn't think she was likely to listen" is correct in that case.
3. This is actually not a past conditional, it is present: talking to yourself in the present. The formula for this is [present condition] + [future result] = If I don't try it on, how will I know if it fits?
4. If you thought this in the past, and decided not to ask him about his twitter, the correct is:
People always say that this [is] a world that [focuses] on one’s appearance, and I WANTED to be a person who COULD see people’s hearts. If I ASKED for his Twitter address, wouldn’t I become the kind of person I don’t like?
If you are thinking this in the present, and have not decided whether to ask him, the correct is:
People always say that this [is] a world that [focuses] on one’s appearance, and I WANT to be a person who CAN see people’s hearts. If I ASK for his Twitter address, WON'T I become the kind of person I don’t like?
Very advanced, I hope this is clear:)