Why did Borden lead Angier to Tesla?

1) Why did Borden lead Angier to Tesla?

Borden tried to mislead Angier by giving his diary, which Olivia acted as she had stolen from Borden, on request of Borden, to make fun out of him proving he (Angier) was no match for Borden. Borden also succeeded by making Angier leave the town for a long time. Considering Angier was the only tough competitor in magic, it bought Borden some time to expand his business in an empty field! The diary which Borden had given was encrypted and Borden knew, misled by the story of stealing, that Angier would take a serious step in order to get the key from Borden to decrypt the diary. Angier had been to Tesla's show of Telas's discovery in a science fair. But considering the risk attached with the show, no spectator stayed there to see it, including Angier. I believe Borden encrypted the diary with a key "TESLA" for no specific reason (casually), and also the word might be catchy for Angier as Angier knew Tesla had discovered something really special (and he did not know what it was!). So Borden might have thought when Angier would see the word Tesla, he would surely think this was the discovery Tesla had made and Borden was using it. Borden's diary read as: "And yes, Tesla is merely the key to my diary, not to my trick. You really think I would part with my tricks so easily after so much."

2) Didn't he know that it would make him more successful?

Borden did not have any idea that Angier would take the name so seriously. Angier thought Tesla knew the way of Transported Man and made Borden one for his show. So he went to Tesla and requested him to make a similar machine he had made for Borden and surprisingly, Tesla could make such a machine for Angier! Borden had no idea what Tesla was capable of. If he knew, he did not take the risk to push Borden to such a famous scientist and would have made the key different.

3) And did the other half not know about the plan, which is why he went to inspect Angier's machine and end up being accused for murder?

Borden (both the brothers) did not have any clue what Angier had come up with from Tesla. That is why one brother went to check the trick. Like I said if he had knew, he would not have pushed him towards Tesla.

4) If it really had been Borden's plan all along, then surely he could've told his twin the complete truth?

Angier's coming up with the new machine was not Borden's plan at all and that can be concluded from the aforementioned facts.

It was explained in the movie. Angier was given a diary, but the diary was fake and sent Angier on a wild goose chase that almost ruined him. Borden had no idea that the wild goose chase worked, so he went to investigate. That's all. There was no intent to entrap and kill Borden. Angier already knew he had the best trick, so there was no reason to do anything else. That why he used blind stage hands. Not to keep the trick a secret, but the result. Basically Angier committed suicide every performance. He "fell" into the tank because Cutter explained that drowning was like "going home" once Cutter exposed the truth about drowning, that gave Angier's 2nd thoughts... but not until the movie ended.