We searched for our friends all morning but couldn't find them.
Мы искали наших друзей всё утро, но не могли их найти.
Мы искали наших друзей всё утро, но не смогли их найти.
Why perfective for мочь? Because the sentence focuses on the result of мочь action, which is unsuccessfull, rather than on the duration of the action.

What time will our bus arrive?
I think at eight-twenty.
No, it will come at quarter to nine.
When it comes, we will tell you.
В котором часу приехет наш автобус?
Я думаю, в двадцать девятого.
Нет, он приехет без четверти девять.
Когда он приехет, мы вам скажим.
во сколько придет наш автобус? - it's pridet because the bus itself comes "on foot" not over some form of transport автобус приедет would mean that the bus comes riding on another form of transportation. By the way, there's no such form as приехет, it's приедет, but either way, it doesn't fit this sentence.
(В котором часу) Когда приедет наш автобус? - You can say приехать for a bus and although в котором часу is a fully correct phrase but I have a feeling that most people here would just use когда or во сколько for that.
Я думаю, в двадцать девятого. - It's better to say в двадцать минут девятого, although I bet people are more likely to say just this - в восемь двадцать
Нет, он приедет без четверти девять.
Когда он приедет, мы вам скажем.

I'm going to Moscow tomorrow. I'll buy something there for my parents.
Я иду в Москву завтра. Я покуплю что-нибудь там для родителей.
this means you are going to Moscow tomorrow on foot - if by transport, you would say "ya edu" покуплю doesn't exist, and куплю что-нибудь sounds weird - it's like "I'll buy whatever"
Я иду в Москву завтра

As said, you use идти if you go on foot there. Which is rather weird in this context if you ask me, because it's usually quite a distance to cover if you want to go from one city to another. So I recommend using this:

Я еду/поеду в Москву завтра.

Я куплю что-нибудь там для родителей.

Что-нибудь is completely okay there, even more than that что-то sounds weird in this context. Also I'd say it like that: Я куплю там что-нибудь для родителей

Going back to что-то vs что-нибудь there. Что-нибудь means that you don't know what you're going to buy there yet, just anything that you will find to be worth buying. Что-то means that you vaguely know what you're going to buy but you don't know exactly what it will be yet. See? That's why что-то is really weird in this context.

One more thing - Я куплю кое-что там - That means that you know what exactly you will buy there but you don't want to name it right now.

Кто-то мне сказал, что вы потеряли свой паспорт.
Да, потерял. Я надеюсь, что кто-нибудь его найдёт
This is ok, except in Russian they say мне говорили or мне сказали, что (literally, "they told me that", but it means the same as "someone told me that").
Here I second that suggestion

You did great. Good job

In conclusion, let's take a closer look at кто-то мне сказал. Here кто-то сказал means that someone specific told you that but you don't exactly remember who that person was.
Кое-кто сказал мне here it means that you exactly remember who told you that, like what the person's name, appearence etc were, but for some reason you don't specify who that was.
Мне сказали here it just implies the fact that you was told something, it doesn't focus on any person who did the telling unlike with кто-то мне сказал example.

Кто-нибудь мне сказал - it would be nonsense because кто-нибудь doesn't imply any specific person, just the whole variety of persons out there. But as you see the сказать action is complete now so it had to be someone specific to perform it. I hope this part is understandble.