Its been a while since I did a visa application but I'm pretty sure you can still complete the online application - another member will no doubt confirm that.
As for the visit to Korea - I'm pretty sure that on the application there is a question asking if the applicant has ever been refused a visa to another country. I can't remember if it also asks about refused entries but it probably does. There will no doubt be a refusal stamp in her passport - you need to know what that says.
When completing such questions you should be completely honest - you never know what information is shared. The most common reason that Thai's are refused entry into Korea is because they suspect they are there to work (without a permit). If that's the case, I don't see why that should be a problem if you are up front about it. If that was the reason for refusal and I was answering that question I would simply say that the Korean authorities suspected the visit was for work - it wasn't but they refused entry. But beware, she might well get a phone call asking about this when the application is up for consideration - make her aware so she's expecting it. That's just an opinion though - what an ECO makes of it is up to them. I've always found that being honest and not trying to hoodwink them is the best policy. Besides, if she lies on the application and its discovered, she will be banned from making another application for either 5 or 10 years - can't remember which.
As for the rest of the application, a foreign wife applying for a visa to visit her husband in the UK can throw up its own unique set of circumstances. There is currently another thread running on the same subject so rather than repeat everything - have a read of this:
For a normal visit visa where you are sponsoring the applicant the main things you need to show are:
That you have sufficient funds to cover all expenses.
That your relationship is genuine.
Evidence of regular contact.
The applicant needs to demonstrate that they will return to Thailand at the end of their visit.
Showing reasons to return can difficult with a normal visit visa application - when its a spouse visiting it can be that much harder. Have a read of that thread.