(1) Even if I live in Japan, I cannot read Japanese.
→ Even though / Although / 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.
→ hard

(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. (alwaysをとる)
When you visit the shop, you will always find it is jammed with customers.

(1) あなたが何を言おうとも、私は彼の言うことを信じます。
【解 答】 Whatever you (may) say [tell me], I (still) believe him [what he says].
【別解1】 No matter what you say, I trust him.
【別解2】 Whatever you say, I still believe he is telling the truth.

(2) たとえ誰が説得に来ても、私は自分の決意を変えることはない。
【解 答】 I will never [not] change my mind [take back my decision], whoever [no matter who] tells [wants / may tell / may want] me to. 
【別解1】 I will never chenge my mind, whatever anybody says [may say]. 
【別解2】 I will not du it, whoever wants [tells] me to.
【別解3】 I will stick to my opinion, no matter who tries to change my mind.
【別解4】 Whoever disagree [may disagree] with me, I will not change my opinion.
【別解5】 No one  [Nobody] can [could] persuade me to change my mind.

(3) 英語が少々聞き取りにくくても、内容がすばらしければ皆が真剣に耳を傾ける。
【解 答】 Even if your English is a little [a little bit / a bit  / slightly] hard [difficult] to understand [to catch], as long as the content (of your speech) is woderful, everyone [everybody] listens [will listen] carefully [attentively] to you [to it].
【別解1】 If the content of your speech is worth listening to, your audience pays [will pay] close attention to it, even if it has a little difficulty [trouble / a hard time] understanding [catching] your English.
【別解2】 Everyone will listento you carefully [attentively], as long as what you (will) say is wondeful, even if you cannot speak English well [fluently] [even if your English pronounciation is a little bad / even if your English communication skills are little bit poor / even if your pronounciation of English is a little bad / even if you pronounce English a little badly]. 

(4) 「どんなに忙しくても睡眠時間だけは確保すべきだ」と考えている人は多い。
【解 答】 Many [A lot of] people think (that) however busy you [they] are [may be], you they] should (at least) get enough sleep [have enough time to sleep].
【別解1】 Many people believe that no matter how busy they are, they should sleep enough.
【別解2】 There are many people who believe (that) you should get enough sleep no matter how busy you are [no matter how busy you may be, you should get enough sleep].
【別解3】 Many people believe (that) sleep is important, even when they are very busy.

(5) どのような仕事を選ぶにしても、仕事と余暇のバランスが大切だ。
【解 答】 Whatever job you (may) choose, it is important to strike [to find / to keep] a balance between work and free time.
【別解1】 It is important to strike a balance between work and leisure whatever you choose as a job [an occupation].
【別解2】 Whatever kind of job you choose, the important thing is to strike a balance between work and play.
【別解3】 Whatever work you choose, a balance between work and leisure is important.


(1) 猿は木から落ちても猿だが、議員が選挙で落ちれば、ただの人なのだ。
【解 答】 A monkey is still [remains] a monkey even if it falls [drops] from a tree, but a politician [a Diet member / a Menmber of Congress / a Member of Parliament] who loses (in) an election becomes (just) an ordinary [a normal] person.
【別解1】 A monkey that [which] falls from a tree is still a monkey.  However, if a politician is defeated in an election, he or she becomes an ordinary person.
【別解2】 Even if a monkey falls from a tree, it is still a monkey, but if a politician loses his seat [loses the seat], he becomes an ordinary person.

(2) 言葉には不思議な力がある。どんなに疲れていても、「ありがとう」と言われるだけで、疲れは吹き飛ぶ。
【解 答】 Words have (a) mysterious [magical / miraucous] power.
【別解1】 There is a mysterious power in words.
【別解2】 What other people say has a great influence on [has a great effect on / has a great impact on / greatly influences] us [you].
【別解3】 There is something mysterious about words.
【解 答】 No matter how [However] tired [exhausted] you are [you may be], if [when] someone (just) says, "Thank you" to you, your fatigue vanishes [goes away / is gone / disappears / evaporates].
【別解1】 No matter how tired we are, if we hear someone just say, "Thank you" to us, we (can) forget (about) our fatigue [feel relaxed / feel fine / feel better / recover from our fatigue / get rid of our fatigue / get our energy back].
【別解2】 No matter how tired we are, (you feel as if [that / like]) your fatigue is relieved just because someone thanks you [ you hear the simple phrase, "Thank you." ].
【別解3】 No matter how tired you are, just the words "Thank you" said to you by others relieve your fatigue.
【別解4】 No matter how tired you are, (a few) words of thanks make you forget about your fatigue.

(3) このごろでは、たとえ現金を持っていなくても、乗り物に乗ったり、食事をして、ちょっとした買い物をすることすらできてしまう。
【解 答】 These days(,) even if you have no cash with [on] you, you can take [use] public transportation [ public transport ], eat out, or (even) do some shopping. 
【別解1】 Nowadays(,) even when you do not have any money with you, you can take the bus or the train, eat at restaurants, and even do a little shopping.
【別解2】 These days(,) even if we carry no cash with us, we can take public transportation, eat out, and even go shopping.

(4) 喫煙はあなたや周りの人の健康によくありません。たとえ大人になっても吸うべきではありません。
【解 答】 Smoking is harmful to [bad for] you and (the) people around you.  You should not smoke even when you are an adult. 
【別解1】 Smoking is harmful to [bad for] your health and the health of those [people] around you.  You should not smoke even when you are old enough (to smoke).
【別解2】 Smoking harms [damages / does harm to] the health of people around you as well as your health.  Even when you are [becomes] an adult [a grown-up], you should not smoke.
【別解3】 Smoking is harmful to people around you as well as to you.  Even when you are old enough to smoke, you should not.

(5) [前半]どんなに科学が発達しようとも、それは生きることの意味を教えてはくれない。
【解答】 However [No matter how] advanced science is [might be / my be], it never teaches [shows] us the meaning of life.
【別解1】 However [No matter how] remarkably [much / far / greatly] science progresses [develops / improves / advances], it will never teach [show] us the meaning of life.
【別解2】 However [No matter how] remarkable [great / much] progress science makes, it never teaches [shows / tells] us why we live [what it means to live / what we live for].
【別解3】 It is true  that himans have made remarkable [great / incredible] progress in science.  However, this does not help us (to) [enable us to / allows us to / make it possible for us to] find [grasp] the meaning of life.
【解 答】 What are we living for?  This is a question (that / which) we must answer for ourselves.
【別解1】 What do we live for?  It is up to individual human beings to find that out.
【別解2】 What do poeple live for?  Each of us individually [Only we] must find an [the] answer to this question.
【別解3】 Each of us individually must find an answer to the question of [that asks] what we live for.