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Jc: no.  This is covered in #3 of the second question, "When are you not allowed to castle?".

Can a king castle if the case where he lands is occupied by an enemy piece (resulting in the capture of that piece)? For example, if the king is in E1, has not moved, the rook with which he castles is in A1, has not moved and there is a bishop in C1, can the king castle?

To Hey_Bryce@yahoo.com, that really just depends on what type of tournament or play it is.  Each chess organization has its own rules about announcing things and how honest mistakes are dealt with.  Generally speaking in blitz games (less than 5 minutes per side), there are some unwritten rules about how illegal moves result in a loss for that player (or it's up to the opponent whether to "forgive" the mistake). 

To comment further on the casual under-5 minute games (aside from the castling question), anyone who moves without noticing he or she is in check can actually have his/her king captured/game over.  The reason is because the opponent shouldn't have to be wasting his or her clock time saying "oh no you can't do that, sorry."

I have a question about castling.  If black is all set up to castle and the white player puts the black player in check.  The white player does not specify black is in check (stating "check" is optional).  The black player does not realize he is in check.  Can black now castle because in his mind he is not in check?  Or if black tries to castle, can white now say "You cannot do that, you are in check"?  thanks

No, there is no re-castling or un-castling in Chess.

Simple Question: Once we do the castelling, if there no check or any other issues, can we re-castle it back to the original position

Holy Ghost!
PS: In the situation I said before is not avoid check, because he could
just not move and move other piece. But he is also not moving his king to
one square kingslide (or queenslide) position, while avoiding check,
because he will not end the turn in this square anyway, his king will end 2
squares kingslide or queenslide

This made me think of this example.
Lets imagine king is not into check, he will not end into check after
castling, but the square he will use to make castling is.
In this case he would be able to just not move his king and avoid check.
So, by making the castle he would not be avoiding check.

I've always imagined it is because castling is intended as a development move for breaking board symmetry, not as an escape move to get out of a serious attack.  If your opponent has already launched an attack on the King's current position, or if (say) he is using a Rook to cut you off from that side of the board, it's considered unfair to get away or to cross the line of control using a special move.

Kind of like how en passant capture was added because the pawn's double-step was intended as a development move to speed up the game, and people didn't like that it was being used to leap past enemy pawns without giving them a chance to intercept, thus altering the game's strategy.

But I could be wrong.

Haha, just kidding last post :)
Yeah look it is good question, why can't the king castle out of check. 
Maybe when they set the rules, on the another day, they could of allowed it. All i can think of, is, castling is like a big production. You move the king 2 squares instead of one, and the rook also moves in the very same turn. Therefore, it cannot be done 'fast enough' to get out of check :)
So yes, i don't know hehe.
As far as why the king cannot move through check, dont know either, all i can guess is, 'the king cannot move into check', the rule see's moving through check as 'being in check while moving' so to speak.
It actually doesn't move (finish) in check though.
Interesting and great question.

What is the idea behind not being able to castle from check and the first
square where king will pass not being able to be into check?

I know the rules states those things are not allowed. But I am asking what
is the idea behind it?

Under 'touch-move' rules, what is the correct procedure for castling?

The king must be moved two squares first. Then the rook is moved. If the rook is touched first, it must be moved and the king may not be moved.

Is it correct that a king or rook may not capture when castling?

As any piece being captured would have to be standing between the king and the rook, it goes without saying that neither the king nor the rook may capture when castling. Indeed, in the above diagram, even though all of the other five requirements are met, white is not allowed to castle.

The Excalibur program must have a bug. Castling is legal in that position.

Or you havenèt reset the castling flag or something like that on the Excalibur (I donèt own one, so I donèt know).

BTW, your Be3 moves are illegal in that sequence you provided, Bd3 is the correct move.

Your c1-Bishop (the one that actually can reach e3) is blocked by the d2-Queen.

In playing black with my Excalibur set, I turned on the board after making
the following moves to explore the Center Game:
1. e4, e5
2. d4, e5xd4
3. Qxd4, Nc6
4. Qd2, Nf6
5. Nc3, Bb4
6. Be3, d5
7. e4xd5, Nxd5
8. Bxh7, Nf6
9. Be3
At this point I turned on the computer, setting up the game's
continuation by pressing 'on/clear,' then 'new game,' then the king
button, then 'mode,' and indicating the locations of the pieces according
to the directions.  I then set 'side' for black to move first, pressed
'clear,' set the level at 32, and pressed 'clear' once more.  I
attempted to castle but the computer did not allow it.  The only reason was
that h7 had been taken, but there is nothing to this effect in the rules of
chess.  Could you explain why the makers of Excalibur have configured the
game in this manner?