(1) My grandfather's hobby is to collect antiques. → collecting
(2) All youhave to do is waiting here. → (to) wait
(3) One of the most important purposes of learning a foreign language is communicate in that language.
→ to communicate
(4) It is impossible that you look after the child. → for you to look
(5) It is important that she knows this fact. → for her to know / that she (should) know
（解答） These days, it is not unusual for Japanese baseball players to succeed in the major league.
（別解） Nowadays, it is common for Japanese players to paly active roles in the major league.
（解答） It is a valuable experience to learn about different cultures when you qre young.
（別解） Being exposed to foreign cultures when you are young is a valuable experience.
（解答） In the Japanese business world, it is customary to exchage business cards with those (whom / who ) you are meeting for the first time.
（別解） In the Japanese business world, people usually exchange business cards with those they are metting for the first time.
（解答） It would be risky to depend on only one ebergy source.
（別解） It is dangerous to depend only on one energy souurce.
（解答） I our society, it may (still) be difficult for fathers to be as involved in rasing children as mothers (are).
（別解） In our society, it seems that it is difficult for fathers to take part in childcare like mothers.
（解答） The best thing about teaching Japanese abroad is that (we are) asked by (our) sutudents (seemingly) simple questions about Japanese and Japanese people, we (often) make unexpected discoveries.
（別解） The greatest satisfaction (that / which) we get from teaching Japanese abroad comes when (our) students ask us (seemingly) simple questions. Thinking about the answers to them makes us discover new things about our own language and Japanese people.
（解答） It is very clever of that crow to build his nest in a tree on a busy street where land prices are said to be the highest in Japan.
（別解） I have heard that a crow has built his nest in a tree on tha main street where land prices are said to be the highest in Japan. How clever (it is) of the crow!
（解答） One of the most bewildering things for foreibners who come to Japan, where pecking orders are highly stressed, is that Japanese advertise themselves too modestly.
（別解） One of the most bewildering things for foreigners who come to Japan, where pecking orders are highly stressed, is that Japanese hardly ever advertise themselves.
（解答） Considering (that) one of the (most important / main) purpose of conversation is to exchange ideas, the first thing to do before startng to speak English is to have your own (definite) opinions (about various things).
（別解） One of the (most important) purposes of conversation is an exchange of ideas. Considering this, the first step of English coversation is to think about what you have to say.
（解答） One of the most important roles of education is to enable young people to deal with any changes in society.
（別解） One of the most important functions of education is to help young people (to) develop their ability to deal effectively with any changes in society.
I believe that you should travel abroad for the following reasons.
Firstly, you can get to know another country through personal experience. Eating the local food, seeing the landscape, art and architecture and communicating with the local people will create a deep impression, quite unlike the merely abstract experience of reading facts about the country in a book, which are soon forgotten.
Secondly, your experience of communicating with people whose way of thinking differs from yours will give you a more objective idea of the good and bad aspects of the society to which you belong.
Thirdly, it will give you a chance to use a foreign language in a practical way and to realize that the language is an expression of the charactor of the people. The memories of your experiences there will make you feel that the language has become a part of you and that you would like to develop this aspect of yourself furter.
In conclusion, traveling to another country will give you a genuine and personal motivation to study foreigb languages and a real interest in foreign countries. This kind of awakening among people is vital to the further of the world.