Bohemian,
In a regular court, eg personal injury, the loser pays the winners costs. This means that if you sue someone for personal injury and win, they pay your fees. They may or may not have insurance for that. (There is also the issue of whether they recover all the costs, but that's a bit of a side point).
In an employment tribunal, each party bears their own costs. The only exceptions are where one party has behaved so unreasonably that the tribunal orders them to pay the costs. However, this relates to the conduct of the litigation (e.g. bumping up costs unreasonably by making loads of unecessary interim applications or whatever), not generally their conduct in relation to the employee in the first place.
As others have said, yes, you would need to be in court at the same time as your boss. He would probably be sitting there while the barrister cross examined you. It isn't really like a court though, more like a big classroom which a bench at one end on a raised platform. No one wears wigs or gowns. However, I am not going to lie to you, it is a blooming scary experience. If you want to go ahead, you need to be prepared for that.
Having said all of the above, if your claim has any merit, your employer will want to settle it. The majority of discrimination claims never make it to a hearing. The majority that do only do so because the employee has unreasonably high settlement applications and didn't take a reasonable offer when it was made. Therefore, you don't need to want to go all the way to tribunal, just to hang on long enough to see what sort of offer you get.
As a result, you have to assume that you will pay your costs if you win. There is no reason for this to come out of the employer's insursance. That money can come (broadly) from one of two places:
-
You have insurance which covers the costs. As others have mentioned, it could be a home insurance policy that covers legal fees.
-
It comes out of what you win.
2 is far more common, which is why you need to be really sure that fighting still gives you more money than settling after the costs are allowed for. Your lawyer would advise you on whether an offer was a good deal.