Is Borden's true identity real, or another ruse?

While this is an interesting idea (and one which others have brought up on this site before, but I'm glad someone finally turned this into a proper question), I think it contradicts both the movie's plot and its overall themes. So no, I don't think there is much evidence in favor of this theory, but there is IMHO very well evidence against it, even if not so hard an evidence (and interpretation is still a free good).

As you yourself stated in your question, Borden and his twin both lived half a life for their entire life. And in turn this is "their real trick and shows true dedication to their art". This is what actually distinguishes Borden from Angier, who always tried to go the easy way and couldn't even imagine devoting his entire life to "just a magic trick". That is why Angier doesn't get behind the old Chinese magician's trick and Borden immediately realizes it, because the Chinese magician also devoted his entire non-stage life to keeping up the actual trick, like Borden did. And this is also the reason why Angier cannot believe Borden to just use a double for his Transported Man, since his own attempts with a double were not that fruitful and didn't work that well in the end, since he just wanted to do it the fast and easy way. So he thought there must be more to it than such a simple secret, but "The secret impresses no one, the trick you use it for is everything" (which might in the end even be the reason why you yourself think there to be more to Borden's trick, he achieved to deceive you, too ;-)).

So given this major theme of dedicating his whole life to his art in contrast to going the fast and easy way to just to do a good show, Borden also using a cloning machine wouldn't really fit that well. And in the end Tesla himself said he never built such a thing, and while we might not believe him, he didn't have so much reason to lie at this point (having previously claimed to have built it until Angier finds out he didn't). And even more important, what would be the reason for Borden to send Angier to Tesla if he knew he could build such a thing, since it was always planned as a distraction for Angier? While the coincidence might strike you as too coincidental, Borden sending him to the actual goal and just pretending it to be a wild goose chase would be much more of a plot-inconsistency. This also doesn't fit to Borden's reaction on this whole setup. He was as surprised as you and me that Angier actually "survived" the supposed murder, so he had absolutely no idea that Angier had a machine for cloning himself, which wouldn't be the case had he known that Tesla could construct such a device.

So that being said let's take a look at Tesla's significance as keyword and the supposed coincidence. There is still a reason for Tesla being used as keyword while coincidentally being able to build that machine, even if not as impressive a reason. In the movie he once was at a science fair or something similar in London, which both Angier and Borden attended as spectators. Borden might very well have seen Angier there and might have seen that Angier was impressed by Tesla's rather innovative science (that might have seemed like magic at that time), while all the others literally ran away in fear. So he thought Tesla might be someone that Angier could really believe to have built such a "magic" machine, which made him a reasonable keyword, given that he lived so far away.

The fact that Tesla could in the end really build such a thing was a coincidence Borden did not anticipate, and was actually an homage to Nikola Tesla's genius, using a bit of an overfictionalized version of the actual historical person. While not being an expert in this topic I know that even the real Tesla has a reputation for being quite an innovative person who had ideas that didn't get the respect or appreciation they deserved at their time (even if a duplication machine was maybe a bit over the top even for him), which also fits to his mythical introduction in the movie and his overall impressing presence (amazingly incarnated by noone else than David Bowie). So if anyone could have built such a machine at this time it would be Tesla and Borden might have been aware of this fact (even if he underestimated him and didn't really deem it possible) and assumed that Angier thought the same. So the writer of the script (or rather the novel it was based on) payed his tribute to the real Nicola Tesla by letting his fictional version achieve true scientific magic, while presenting quite a surprising, well yeah, coincidence to the audience. It wasn't so much a coincidence more than Borden and all of us just underestimating the genius of Nikola Tesla, like real history might have done, too.

It should be noted that while Tesla was not responsible for Borden's trick, he did in fact make a machine for Borden, who in one scene uses a Tesla Coil on stage during a performance. So clearly Borden took a real interest in Tesla, enough to purchase one of the man's electrical devices. Thus, we have further evidence that Borden's use of Tesla as the keyword to his notebook was perhaps genuine and not merely a ruse.

Were Borden and Fallon real twins?

Yes they were real twins. They were there from start, that is the reason Bordon was not able to answer the question when Angier asked which knot he tied to his wife, as it is possible other brother was present.

As per wiki, quote from wiki:

He then realizes that "Borden" was actually identical twins who shared their lives on stage and off. Just as they took turns being the man in the box and the prestige, they took turns being Borden and (by wearing makeup) Fallon. When one twin lost his fingers because of Angier, the other had his brother remove his own so they could continue to look alike in order to keep up the illusion there was only one Borden. One twin (the one alive) loved Sarah and was the girl's father, while the other twin (the one hanged) loved Olivia. So they each had half of a full life, which was enough for them but not for the women they loved.

Borden sends Angier to off trail by tricking him into wasting time with Telsa, so that Angier will not realize that they are twins. He was just trying hide his trick that they are twins. As added advantage, he sent Angier out of town chasing something of no use, getting no big competition for quite a time.

As to the overall themes of the story, it seems more likely that Bordens were twins.

As to anyone who personally knows more than one pair of identical twins - there are always some physical differences between them, even if you disregard all behavioral aspects. No identical twins are literally identical. There are always some really subtle differences, like a few birthmarks being different for instance. Even if the Bordens didn't share "their" wife in bed, eventually she would have seen both versions enough to notice these tiny physical details changing from day to day.

The only way to remove this major plot hole is if they were clones, not twins.

Also, at some point in their early life would've had to decide to become magicians and perform a trick such as the transported man. From there on, they would have lived as Fallon and Alfred for a very long time. They would have needed to move off far away so that no one who knew them as twins could have come in contact with them to blow their cover. In the movie, Borden seems to think of the transported man trick after meeting his wife, whereas actually, he would've been planning it already for years. Of course, he could also have been acting.

My interpretation is that Borden originally cloned himself only once using Tesla's apparatus, and subsequently shared his life with the clone.

Angier wanted to know Borden's secret, so Borden cryptically answered by Writing 'Tesla'.

Angier then went to Tesla ultimately to be cloned, but presumably he didn't want to share his life with a clone, so he resorted to cloning himself at every performance of his illusion and killing either the clone or himself each time.

I think it is supposed to be open for interpretation.

There are plot holes with both solutions. For example, if they are twins, then how come Fallon is introduced so late in their life? They would have to plan it from their childhood so how come Fallon didn't exist when they moved out on their own? Where would the other twin go during a show before Fallon? On the other hand, Tesla says he had never made a machine like the cloning machine before. He also was very against it after he made it, but why did it take him so long to realize it? If he made it for Borden, it would have existed for years.

Maybe it's just supposed to be a mystery