1. He is well known (both) at home (and) abroad.
2. It is (not) cars (but) the users that I am concerned about.
3. (Whenever) I visit her at the hospital, I take some flowers.
(Every) (time) / (Each) (time) I visit her at the hospital, I take some flowers.
4. Helen Keller was (not) (only) blind (but) (also) deaf.
Helen Keller was deaf (as) (well) (as) blind.
(Besides) being blind, Helen Keller was deaf.
5. You can have (either) chicken (or) fish, but I would recommend the chicken.
6. Further delay is (neither) necessary (nor) desirable.
7. This problem is (too) difficult (for) (me) to solve.
This problem is (so) difficult (that) I cannot solve it.
This is (too) (difficult) a problem (for) (me) to solve.
This is (such) a difficult problem (that) I cannot solve it.
8. (On) seeing me, he grew pale and ran away.
(As) (soon) (as) he saw me, he grew pale and ran away.
(The) (moment) / (The) (instant) he saw me, he grew pale and ran away.
(No) (sooner) had he seen me than he grew pale and ran away.
(Hardly) / (Scarcely) had he seen me before he grew pale and ran away.
9. (Though) he is clever, he is backward in giving his view.
Clever (as) he is, he is backward in giving his view.
(For) all his (cleverness), he is backward in giving his view.
(In) (spite) (of) his cleverness, he is backward in giving his view.
10. To the best of my (knowledge), this is the shortest way to the airport.
As (far) as I know, this is the shortest way to the airport.
11. (However) hard he tried, he couldn't solve the problem.
Try hard (as) he might, he couldn't solve the problem.
☆ つづり字や括弧の数に関しておかしい様に思う個所がいくつかありましたので、勝手に修正して回答しました。問題の本文と比べて下さい。また、複数回答の可能性のある部分は、スラッシュ(/)を使っています。