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Okay...so we agreed that Eun Ho's vision was blurry? Then why was it blurry? Because it was not yet set in motion. Accident happened...WS in hospital and Eun Ho got a clear vision of what she saw in the mall...SY's rise to fame.
Why was it clear now? Because the accident had set in motion the fruition of SY's destiny that he was born with...according to the deity..."to rise high and burn out quickly". The accident did not switch WS's and SY's fates...they both had continued to lived the lives that they were born to have...until Eun Ho granted WS's wish. And this is why deity's reveal in episode 10 was important...it was to clear up the ambiguity of Eun Ho's initial blurry vision and whose fate she thought she saw.
Yes, the deity did point out the consequence of that accident...the driver died before his time...which in turn affected his family...which Eun Ho found out in episode 10...whereby she tried to make amends by financially assisting both his wife and daughter.

By "he" are you referring to the deity? Are you saying he got it wrong? I guess he could be lying to Eun Ho in episode 10, but why would he? What would he gain?
WS's fate to be famous and play for Korea was based on what? Eun Ho's vision at the mall? The blurry one where we couldn't even tell whose face it is? I think Eun Ho assumed it was WS's...unless she actually had a clear vision of him whereby, we, the viewers, were not privy to.

No probs. I don't think they could have given you the deity's reveal until WS found out he was going to die...which is what happened in episode 10.

If the deity is to be believed, he said that WS was born to live a long but difficult life and SY was born "to rise high, but burn out quickly"...and this is exactly how they both were living their lives before Eun Ho granted WS's wish. WS getting hit by Lee Yoon's car did not change his original fate, but with Eun Ho's meddling, it did...he's now living SY's life..."to rise high, but burn out quickly". However, the accident did changed someone else's fate...the driver's...he died before his time.

Actually Eun Ho's first vision, in the mall, was blurry...unless it was meant to be blurry to keep us in the dark about what she actually saw. Her second vision, in the hospital, definitely showed SY as the one who will become famous. As to why did she thought, from her first vision, that it was WS's? It was based on two things...she presumed SY was bookish and not an athlete by the ease that she bounced him off her, and the vision came to her after she locked eyes with WS.
Why was WS sought after and not SY?
Not because WS was more talented, but most likely because his Dad greased the palms to make it happen. For example, SY was not allowed to play to his full form, instead, he was punished for not letting WS shine in front of the National Team coach. Preferential treatment not talent.
Did the accident changed anything?
No, but that accident probably simply pushed SY's fate to happening sooner than later. Plus it propelled Eun Ho's fate to becoming a human.

In episode 10, the deity explained that WS and SY were living the lives that they were born with (their fates)...until Eun Ho switched it around.

Eun Ho's first vision was not clear...if what was shown to us was exactly what she saw...because the face of whose fate it belonged to was blurred. However, if you look closely you will see it was SY's...which was confirmed by the deity when he said that for SY, the fate that he was born with was " to rise high and burn out quickly" while for WS, his fate was to live a "long and difficult life". Her second vision...after WS's accident...clearly showed that SY was the one who will become famous. Did the accident caused their fates to change? From what the deity said, it didn't. Why? Because it didn't matter how they got there...such as the accident...as long as the end result was for them to lead the lives that they were fated with...until Eun Ho switched it around.

The deity said that Si Yeol's fate was "to rise high, but burn out quickly" while WS's was to have a "long and difficult life" ... which meant that they were both living their fated lives before Eun Ho's switched it around. Now to revert it back, she has to kill Si Yeol with the dagger before WS dies...which in turn will let her return to her 9-tailed life.

Eun Ho's vision (if what we saw is exactly how she saw it) did not clearly show that WS was the one fated to be famous...the face was blurred...but after rewinding and pausing several times, I believe it was actually Si Yeol's fate she saw. This is actually confirmed in episode 10 when the deity said that Si Yeol's fate was "to rise high, but burn out quickly" while WS's was to have a "long and difficult life"...until Eun Ho's switched their fates to what it is now.

I think there was theory going around about those were the memories that Si Yeol will lose once his fate is changed back.

I believe it was explained in episode 1 around 44:50 where there were only 2 choices for a 9-tailed fox.