Quote Originally Posted by Mr Smith View Post
1. Туристический маршрут <<Золотое кольцо>> проходит по древним русcким городам: Ростов, Ярославль, Кострома, Владимир, Суздаль.
1. The Tourist route “The Gold Ring” goes (passes) along the ancient Russian towns: Rostov, yaroslavl, Kostroma, Vladimir, Suzdal.

2. Эти города известны своими памятниками русской культуры.
2. These towns are well known for their monuments of Russian culture.
OK!

Quote Originally Posted by Mr Smith View Post
3. Питер давно хотел поехать по этому маршруту.
3. For a long time, Peter has wanted to go along this route.
Maybe, проехать? Although "поехать" is still possible, "проехать" fits better.
"Проехать" emphasizes the whole way, while "поехать" is more like "start going".

Note: in sentence 5 we definitely have "поехать" (not "проехать"), because sentence 5 tells us about their departure.

Quote Originally Posted by Mr Smith View Post
4. И вот, наконец, ему повезло: Саша купил машину
4. And here (now?), finally, he is lucky: Sasha bought a car.
In this occasion "вот" is a particle which can hardly be translated. The whole expression "и вот" at the beginning of a phrase conveys the idea of "finally". The next word ("наконец") is pretty much the same as "и вот". But the combination is quite natural for colloquial speech: "И вот, наконец, ..." - "вот" is used to emphasize "наконец". So, I would translate it into English as "And finally, he is lucky ...".

Quote Originally Posted by Mr Smith View Post
5. Теперь они могут поехать туда на машине
5. Now they are able to go there by car.

6. Они выехали из Москвы рано утром, когда на дорогах ещё мало движения
6. They drove out of (departed from) Moscow early in the morning, while traffic was light (there was still little movement on the road).
OK!

Quote Originally Posted by Mr Smith View Post
7. Саша вёл машину отлично, и через два часа они подьезжали к Загорску
7 Sasha drove (led) the car excellently, and within two hours they were approaching Zagorsk.
Note, it is "подъезжали" (hard sign ъ, not soft sign ь).

Quote Originally Posted by Mr Smith View Post
8. Теперь он называется Сергиев посад
8. Now it (Zagorsk) is called Sergei Posad.
OK!

Quote Originally Posted by Mr Smith View Post
9. Они решили не заезжать в Сергиев посад, но было приятно проехать мимо древнего города.
9. They decided not to call in (take a side trip to) Sergei Posad, but it was splendid to drive past (pass through?) the ancient town.
Here, "проехать" means "to drive past" or "to pass by" or even "to pass through". Note: this usage of "проехать" is different from the usage I proposed for sentence 3. In sentence 3, "проехать" is "to drive the whole way".

Quote Originally Posted by Mr Smith View Post
10. Часа три они ехали по Русской равнине
10. For three hours they drove along the Russian plane.
Not just "for three hours", but "for about three hours".
Compare: Три часа = Three hours; Часа три = About three hours. When you swap a number and a noun (like "часа три"), it means rough approximation.

Quote Originally Posted by Mr Smith View Post
11. Дорога была очень ровной и немного однообразной.
11. The road was very flat/ even and a little monotonous.
OK!

Quote Originally Posted by Mr Smith View Post
12. И вдруг посреди равнины, когда они подьезжали к Ростову, перед ними открылся замечательный вид: озеро Неро и на берегу белокаменный город.
12. And suddenly, when they were approaching Rostov, in the middle of the plane before (in front of) them, a magnificent view revealed itself: Lake Nero and, on the shore, a town built of white stone.
Again, it is "подъезжали" (hard sign ъ, not soft sign ь).

Quote Originally Posted by Mr Smith View Post
13. Они долго ходили по городу.
13. They walked up and down/ around the town for a long time.
OK!

Quote Originally Posted by Mr Smith View Post
14. Несколько раз обошли со всех сторон знаменитый Ростовский кремль и сфотографировали его, попросили рыбака перевезти их на лодке на другой берег озера и оттуда снова фотографировали всё.
14. Several times (they) walked around (encircled) all of the sides of the famous Rostov Kremlin and photographed it. They asked a fisherman to take them (transfer them) across to the other coast of the lake by boat. And, from there, again, (they) photographed everything.
I think it should be "... и оттуда снова сфотографировали всё." You started with perfective in the first part of the sentence ("... обошли со всех сторон знаменитый Ростовский кремль и сфотографировали его ..."), and it seems logical to keep perfective in the second part. Not you, of course I mean the textbook. But anyway, I would use "сфотографировали".

Quote Originally Posted by Mr Smith View Post
15. У входа в собор они разговарились с симпатичным стариком.
15. By the entrance in the cathedral, they conversed with a likable old man.
15. ‘в собор’ if this is supposed to mean ‘in the cathedral’, should it not be in the prepositional case?
"By the entrance to the cathedral..."

No, "в собор" should be in accusative, since it relates to "вход" (entrance): "вход куда?" (entrance to where?) - "вход в собор" (entrance to the cathedral). "У входа" is static location (where they conversed), but "в собор" is direction related to "entrance". Maybe, it was not even INSIDE the cathedral, it could have happened outside of it (but by the entrance TO IT).

Compare: "В соборе они разговарились с симпатичным стариком." = "In the cathedral, they got into conversation with a likable old man."
but "У входа в собор они разговарились с симпатичным стариком." = "By the entrance to the cathedral, they got into conversation with a likable old man."

BTW, "разговориться" (perfective) is more like "to get into conversation", "to find plenty to talk about".

Quote Originally Posted by Mr Smith View Post
16. Его звали Иван Кузьмич Травкин.
16. He was called Ivan Kuzmich Travkin.
Or, in English you can just translate it as "His name was ...".

Quote Originally Posted by Mr Smith View Post
17. Иван Кузьмич Оказался местным историком и рассказал им много интересного об истории древнего города.
17. Ivan Kuzmich turned out to be a local historian and (he) told them many interesting (things) about the history of the ancient town.
OK!

Quote Originally Posted by Mr Smith View Post
18. Они узнали, что Pостов существовал уже в седьмом веке, и что в древние времена через него проходила дорога на Восток.
18. They found out that Rostov already existed in the seventh century and that, in ancient times, a road went through it (проходила) to the east.
OK!

Quote Originally Posted by Mr Smith View Post
18. I am confused by the use of ‘через’ and ‘проходила’ in this sentence.
What exactly confuses you? "дорога проходила через него (Ростов)" = "a road went through it (Rostov)". You translated it right, why is it confusing for you?

Quote Originally Posted by Mr Smith View Post
Also, why is ‘проходила’ in the feminine? I thought it should agree with ‘Pостов’, which is masculine?
Because "проходила" relates to "дорога": "дорога проходила через Ростов".

Quote Originally Posted by Mr Smith View Post
19. Вместе с ним они вошли в собор и долго рассматривали фрески неизвестного художника.
19. Together, with him, they entered the cathedral and, for a long time, (they) examined the Freskos of an unknown artist.

20. Иван Кузьмич ехал в соседнюю деревню, и Сашa с Питером были рады подвезти его.
20. Ivan Kuzmich was going to a neighbouring Village, and Sasha and Peter were pleased to give him a lift.
OK!

Quote Originally Posted by Mr Smith View Post
21. Правда, соседняя деревня оказалась далеко, и только к вечеру они довезли Ивана Кузьмича до его деревни.
21. In truth, the neighbouring village turned out to be far (away), and they only got Ivan Kuzmich to (as far as) his village by the evening.
OK!

Quote Originally Posted by Mr Smith View Post
21. Please offer an alternative translation of this sentence.
I'd say the translation is right. What don't you like in it? Why do you need an alternative one?

Quote Originally Posted by Mr Smith View Post
22. Было уже поздно, когда они приехали в Ярославль.
22. It was already late when they arrived in Yarislavl.
OK!