First sentence
まいばん くにの かぞくに でんわします。
I call my family at my home country every evening.
First of all, the family is not making the call, but someone (probably the speaker, it could be someone else) is making a phone call to the family, because it is marked with the particle に. The particle に marks the goal or destination of the action, in this case, whom the call is made to.
国【くに】の家族【かぞく】 is used to talk about the family you have in your country of origin or homeland. Presumably, the speaker is now in a foreign country and makes a phone call to his family who are living at his home country.
Your answer is correct. We know that:
1 - The answer must be either the 1st or the 3rd sentence because they start by よる (evening/night), and in the original sentence it is said まいばん (every evening). 2nd and 4th don't make sense because they start by あさ (morning).
2 - The answer must be either the 3rd or the 4th sentence because they use いつも (always), and in the original sentence it is said まいばん (every evening). If it is every evening, then it is always. 1st and 2nd don't make sense because they use ときどき (sometimes).
So, the only option that is coherent with the time (よる) and the frequency (いつも) is the 3rd sentence.
Second sentence
このまちにはゆうめいな建物があります。
In this city there is a famous building.
You interpreted the second sentence correctly, although I'd say "In this city there is a famous building" rather than "this city has a famous building", because the verb ある means "to exist, to be". Anyway, the final meaning is the same.
You are right about the answer, too. It is the first one because it is the only that talks about a building (建物/ビル). The sentence structure is the same for the four options, it just replaces the word ビル by other substantives.
I think you are doing pretty well, just keep learning new vocabulary and you will see how you figure out this kind of exercises more easily.
As a reference, I write down how I would translate each sentence so you can understand them better.
よる は ときどき くにのかぞくにでんわします。
At night, I sometimes call the family at my country.
あさ は ときどき くにのかぞくにでんわします。
In the morning, I sometimes call the family at my country.
よる は いつも くにのかぞくにでんわします。
At night, I always call the family at my country.
あさは いつも くにのかぞくにでんわします。
In the morning, I always call the family at my country.
このまちにはゆうめいなビルがあります。
In this city there is a famous building.
このまちにはゆうめいなおちゃがあります。
In this city there is a famous tea.
このまちにはゆうめいなケーキがあります。
In this city there is a famous cake.
このまちにはゆうめいなこうえんがあります。
In this city there is a famous park.