(1) Even if I live in Japan, I cannot read Japanese.
→ Even though / Althouth / Though
(2) However you run fast, you will not be able to catch up with me.
→ However fast you run
(3) However much I tried, I could not solve this problem.
(4) Whatever will happen to you, don't forget that I'm with you.
→ happens [may happen]
(5) Whenever you visit the shop, you will always find it is jammed with customers.
→ Whenever you visit the shop, you will find it is jammed with customers.
（解答） Whatever you (may) say, I (still) believe him.
（別解） No matter what you say, I trust him.
（解答） I will never change my mind, whoever tells to me.
（別解） I will never change my mind, whatever anybody says.
（解答） Even if your English is a little hard to understand, as long as the content (of your speech) is wonderful, everyone listens carefully to you.
（別解） If the content of your speech is worth listening to, your audience pays close attention to it, even if it has a little difficulty understanding your English.
（解答） Many people think (that) however busy you are, you should (at least) have enough time to sleep.
（別解） Many people believe that no matter how busy they are, they should sleep enough.
（解答） Whatever job you (may) choose, it is important to strike a balance between work and free time.
（別解） It is important to strike a balance between work and leisure whatever you choose as a job.
（解答） A monkey is still a monkey even if it falls from a tree, but a politician who lose (in) an election becomes (just) an ordinary person.
（別解） A monkey that falls from a tree is still a monkey. However, if a politician is defeated in an election, he or she becomes an ordinary person.
（解答） Words have (a) mysterious power.
（別解） There is a mysterious power in words.
（解答） No matter how tired you are, if someone (just) says, "Thank you" to you, your fatigue vanishes.
（別解） No matter how tired we are, if we hear someone just say, "Thank you" to us, we (can) forget (about) our fatigue.
（解答） These days, even if you have no cash with you, you can take public transportation, eat out, or (even) do some shopping.
（別解） Nowadays, even when you do not have any money with you, you can take the bus or the train, eat at restaurants, and do a little shopping.
（解答） Smoking is harmful to you and (the) people around you. You should not smoke even when you are an adult.
（別解） Smoking is harmaful to your health and the health of those around you. You should not smoke even when you are old enough (to smoke).
（解答） However advanced science is, it never teaches us the meaning of life.
（別解） Nowever remarkably science progresses, it will never teach us the meaning of life.
（解答） What are we living for? This is a question (that / which) we must answer for ourselves.
（別解） What do we live for? It is up to individual human beings to find that out.