I just landed at LAX and the flight attendant (who had a slight Latino accent, but was a native or near-native English speaker) gave the last announcement:

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> "As we prepare to land please have cups and other items ready to throw away, as we're going to make one last pass through the cabin *at which time*." Full stop.
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There were several such utterances during the flight which ended with "at which time," each of which was clearly meant to signify "at this time." Is this a common usage in a variety of English I'm unfamiliar with, or is it more likely to be this one speaker's quirk?
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In this context, the word "suppose" means "believe"; see [Merriam-Webster](http://www.merriam-webster.com/dictionary/suppose):

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> b (1) : to hold as an opinion : believe [they *supposed* they were early]
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> (2) : to think probable or in keeping with the facts [seems reasonable to *suppose* that he would profit]
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So the key phrase:

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> "...the proudest of men, the philosopher, supposes that he sees on all sides the eyes of the universe telescopically focused upon his action and thought."
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...may be treated as:

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> "...the philosopher supposes (believes) that he sees (on all sides) the eyes of the universe."
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Note that the philosopher *is* the "proudest of men" in this sentence; they are the same person.

So, yes, the "proudest of men" believes that the whole universe is fixated on him.
You are pretty correct in your assumption of what this sentence means. The author is comparing the proud to porters, saying that everyone wants an admirer. Nietzsche goes a step further to say outright that philosophers are the proudest men, and that they want the universe to admire them.

Onward, to definitions. To *suppose* something is to assume it as truth. Nietzsche here is saying that philosophers (the proudest men) already assume the universe admires them. 

As for "all sides", the philosopher sees all sides around him looking on. Going back to that pride (a pretty common motif for Nietzsche), the philosopher sees himself at the center, and all sides around that center are focused on him.