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[impeccableman]

"The bus is approaching him at top speed."
Q1: Pete said that it is grammatically correct to add "a" before "top speed"?
Does the two have any differences? Which one is more common?
Q2: Is that "...at a top speed of 70km/hour" grammatically correct, whereas
"... at top speed of 70km/hour" grammatically incorrect?

"Yes we should all keep our eyes on the traffic lights and not decide whether it is safe to cross a road simply by looking at the traffic."
Q3: Can I say ".... all keep an eye...."?

"Special health drinks may seem like the best solution to the problem of dehydration."
Q4: Refer to the previous posts, Pete said that "That sentence would sound more natural to me with 'for', instead of 'to'...".
I'm not quite certain if Pete was referring to "... to the problem of dehydration" or "... to dehydration". That is to say, I would like to know if Pete mean that "the best solution for the problem of dehydration", or " the best solution for dehydration", or both, would sound more natural?

[archfiends]

"The bus is approaching him at top speed."
Q1: Pete said that it is grammatically correct to add "a" before "top speed"?
Does the two have any differences? Which one is more common?
Q2: Is that "...at a top speed of 70km/hour" grammatically correct, whereas
"... at top speed of 70km/hour" grammatically incorrect?

"Yes we should all keep our eyes on the traffic lights and not decide whether it is safe to cross a road simply by looking at the traffic."
Q3: Can I say ".... all keep an eye...."?

"Special health drinks may seem like the best solution to the problem of dehydration."
Q4: Refer to the previous posts, Pete said that "That sentence would sound more natural to me with 'for', instead of 'to'...".
I'm not quite certain if Pete was referring to "... to the problem of dehydration" or "... to dehydration". That is to say, I would like to know if Pete mean that "the best solution for the problem of dehydration", or " the best solution for dehydration", or both, would sound more natural?

1. I think both is OK. We usually use art. before singular noun as a limitation to make sentence clear and easy to understand, one of my grammatical teacher said that whenever I use a singular noun except proper noun, I have to add an art.(including the, a, an, etc.) . In your example, use a top speed seems more natural to me, but the word 'top' came be the limitation to 'speed' too.

2. Both is proper and OK. You can even use to keep one's eye on something, although it is not proper in gramatical.

3. All is OK too.Reversely, I consider 'the best solution to the problem of' blah. blah. blah. is natural, as well as of or for in this care.

In deed, there is slight different among them, if you use of, the phrase 'the solution of the problem of' seems combined together and will naturally followed with 'can be blah. blah. blah'. Meanwhile 'the solution for the problem of' emphasize the defination of solution, may be following the name and explanation of solution, or followed with 'is blah. blah. blah'. To is much like for, but less powerful in empasize the purpose of the solution.

However those slight difference can hardly be distingushed in sentence.You should judge what to use by your feeling.