『２條英文語法問題..........

1. The correct choice would be the SECOND sentence.

Explanation: Since the last sentence mentioned that (but failed to do so). That means he had already failed to solve the problem and he expressed the sentence at that time.
In this situation, we use the present perfect tense. It means that someone planned or finished something before, but he\she has not done so or fail to do so. Understand???

2. The correct choice would be the SECOND sentence.

Expanation: This sentence is talking about imaginary situation. In this sentence, after if, we use the PLURAL form to express imaginary situation of some people. Understand?

I think both of them are not quite right but if I have to pick one I'll say the first one.
The reason for me to say the first one is wrong is he has not specified a time period in the first sentence. For the second sentence, the word 'have' should be 'has' and should be placed the word, 'planned'. There is also no need to use a comma and the auxillary word 'has' has to be added to the sentence, i.e. He has planned to solve the problem but has failed to do so.

The second one is correct as he is not really a lecturer. It is a hypothetical situation.

for the first question, "He planned to solve the problem,but failed to do so" would be the correct answer. Any verb (i.e. SOLVE in this sentence) after TO should be in present tense.

for the second question, the correct choice would be "He looks as if he were a lecturer. " The word AS IF means "just like ", which implies he's not really a lecturer. When you talk about something not real but just LOOKS LIKE it, use the past perfect tense.