How is the sentence "The symbol % is used to represent percent" read?

All symbols prepresent a shorthand and as such were never intended to be spoken except in cases like "I gave 100%" where 100% can be spelled out as "100 percent" with no awkwardness at all in spoken language.

Your examples containing "symbol %" or "symbol: %" could be invereted and articulated with pretty adequate results if you invert the verbalization to "percent symbol". However your example sentence: "The symbol percent is used to represent percent." evene when inverted to "The percent symbol is used to represent percent.", begs for an illustration to make things clear. (Stand close to a white board.)

In summary, if you change "% symbol" or "symbol %" to "percent symbol", you should be fine in verbalizing them; however, be aware that this symbol doesn't always represent "percent" out side of a math class. You often see common symbols used with with other meanings in other disciplines such as computer science.

I not yet cencounter symbols in heavy use without proper names, but often these go unexplained in a given discipline. I was lucky enough early in my education to have study Greek and locate a history book on the IPA (International Phonetic Alphabet) that helped me resolve a lot of the symbol mysteries.

You can't really read the first 2 sentences out loud.

They are clearly written to be read rather than listened to because they are showing you what a percent sign looks like.

If you were speaking, and trying to tell someone what the percent sign looks like, you might start by saying something like "The percent sign is used to represent percent," but then you'd have to go on to describe what the percent sign actually looks like, or point to one if that were an option. Otherwise what's the point of that sentence?

The point is, the '%' in these sentences does not stand for "percent" because they are all telling you that the symbol stands for that. To do that, the '%' actually has to be standing for itself, the symbol. It's showing you.

So you could read it out loud and say "percent sign" or somesuch at that point, but the visual information which is essential to the whole point of the printed sentences would be lost. So there's a sense in which you'd not actually be "reading it out loud".

I think the closest you could get to preserving the meaning is by doing what I mentioned above, and saying something like,

"The symbol which is formed by a diagonal line from bottom left to top right with small zeros above and below the line is used to represent percent".

And similarly for the second sentence.

I think sentence three is different, because it's not explicitly introducing the symbol, just using it to identify a particular key. It's almost certainly been introduced already and so it's fine in that one to say "percent" at that point. Personally I'm far more used to it being called the "percent sign", but "percent sign symbol" would be redundant and silly.