1-3 are OK.
4: а = "in contrast to": "А я ..." = "And as to me, I ..."

6: approximately "ты знаешь" and "ведь" mean the same in this context. But they can be even combined:
Ты знаешь, я ведь сейчас ни о чём не могу говорить, кроме Петербурга.
"Ты знаешь" is to draw the attention. "Ведь" emphsizes that the fact is obvious. Or it can be close to "the matter is ...": "You know, the matter is I cannot ..."

8. Я никогда не была там, но твои описания так напоминают Петербург!
Note: it is твои (plural form, because of описания), not твой (singular masculine)!

Why is ‘напоминают’ in ‘Они’ form? - Because of "твои описания" - your descriptions. You can also say: "но твоё описание так напоминает Петербург" - the meaning is just the same.
I think the author chose plural (descriptions) to emphasize the fact that the story was long.

10. Ведь Петербург расположен нa ста пяти островах, в городе около трёхсот мостов. (corrected a typo)

13. Какой она интересный человек, и какая трудная у неё была жизнь!

Use of ‘Какой’ is not clear to me. Is ‘Какой’ being used as an emphatic particle in the above context? - Yes!
13.2 What an interesting person she is, and she has had such a difficult life! - Right!

You can rephrase it the following way:

Какой она интересный человек, и какая трудная у неё была жизнь! = Она такой интересный человек, и у неё была такая трудная жизнь! - The meaning is exactly the same.

For example,
Ты такой интересный собеседник! = Какой ты интересный собеседник! = What an interesting interlocutor you are!
Сегодня такая хорошая погода! = Какая сегодня хорошая погода! = What a nice weather it is today!

14. Ей девяносто лет, но она помнит все события, которые произошли за её долгую жизнь, имена всех людей, с которыми она встречалась. (corrected a typo)

16. Она училась тогда в школе, увлекалась поэзией.

She studied then in school, (and) was keen on poetry.
"тогда" = then, that time.

17. На одном из литературных вечеров она познакомилась с молодым поэтом, моим дедушкой и вышла за него замуж.
On (during) one of the literature evenings (or parties?) she became acquainted with a young poet - my grandfather - and she married him. - It is assumed it's like an evening party.
Why is ‘моим дедушкой’ in the instrumental case? - because it is a clarification to "с молодым поэтом", which is in the instrumental case:
"... она познакомилась с молодым поэтом (моим дедушкой)" - I have put it into brackets for more clarity.

19. Всё изменилось в тридцатые годы. ("тридцатые" in plural, because of "годы")

21. Дедушку арестовали, и долгое время она ничего не знала о нём. (corrected a typo)

22. Представь себе она осталась одна с тремя детьми.
It looks almost like it could be an imperative, but it hasn’t followed the spelling rules illustrated in my textbook. Is it an imperative formed irregularly? - It IS imperative. I do not know what are the spelling rule in your textbook, but it is regular:
поставить -> поставь
ставить -> ставь
заставить -> заставь
отправить -> отправь
направить -> направь
готовить -> готовь
etc.

‘детьми’ is unfamiliar to me, here. - it is plural instrumental

If I had been constructing the sentence myself, I would have naturally selected the genitive plural form of ‘ребёнок’, ‘детей’. I cannot see why ‘детьми’ is formed in the way it is. -> You need instrumental because of the preposition "с": с тремя детьми (both "тремя" and "детьми" are in the Instrumental case); but: "без трёх детей" (without three children) - now it is genitive.

31. Казалось, всё будет теперь хорошо.
31.1 It seemed (like) everything was going to go well (at the time).
31.2 All seemed to be going well, now. - No, in this case we would say: "Казалось, всё теперь хорошо" (without "будет") - if I understand your English sentence right. Do you mean "now" is the moment of the story passage (i.e. in the past)? Or do you mean it is actually "now" (2012)?

This sentence is slightly unclear to me. - I think it is because Russian and English follow different tense agreement patterns.
In English, you say: "He told me that he would come" ("told" in the Past, and "would come" in the special tense, Future in the Past).
Russian does not have that Future in the Past, we just use Future: "Он сказал мне, что он придёт" - here the future form (придёт) is viewed from the point in the past. So, it is quite possible he has come already, but then (in the past) it was considered future.

Similarly, the word "теперь" should be understood from the point of view of the moment described (i.e., if it was, let's say, in 1945, then "теперь" in the subordinate clause just refers to the moment of 1945).

So, the main clause "казалось" gives you a reference frame (the past). Everything in the subordinate clause ("казалось, что ...") is already in that reference frame.

32. Но он вскоре умер.
32.1 But he soon died.
32.2 But he died shortly after (those events).Yes, it is shortly after those events. As I explained it in 31), in Russian you have a "reference frame" when talking about events in the past. From the point of view of that reference frame, it was "вскоре".

BTW, in my turn, I do not understand, if there is any difference between English sentence 32.1 and 32.2?

33. С тех пор она никуда не хочет уезжать из Петербурга.
33.1 Since then, she has not wanted to leave St. Petersburg.
33.2 Since then, she has not wanted to go anywhere (никуда), or to leave St. Petersburg .
As to me, the both translations mean the same
Since then, she has not wanted to go anywhere from St. Petersburg.
or
Since then, she has not wanted to leave St. Petersburg for anywhere.

Are they different for you?

36. Передавай привет всем друзьям: Генри, Майку, Маргарет и Су!
Convey/ communicate/ impart my [informal greeting] to all the friends: Gerry, Mike, Margaret and Sue.
To all my friends? Your friends? Our friends? - It is not specified explicitly. Russian just does not require to specify it. But I think both of them (who writes the letter, and who reads it) know those names. So, it is not necessary (for them) to specify WHOSE friends are assumed. Most likely (as I think), they are their common friends. But Russian grammar allows to leave it out.

37. Жду ответа! Всего хорошего! Целую! Твоя Марина
I await your response (answer)! All the best! I kiss you! Your Marina!
Would a letter include all of these endings, or just one? - It only depends on one's personal preferences

‘Целую’ Can someone offer a short explanation of this ending. - LOL! You confused two homographs (words with the same spelling, but different pronunciation and different meaning):
1. целую (stress on "е") - singular feminine accusative of "целый" (whole);
2. целую (stress on "у") - 1st person singular present tense of "целовать" (to kiss) - a typical ending of a letter to a close person (father, mother, son, daughter, beloved one).


The rest of the sentences seems to be OK.