it is cheating if play with bord?

Nope...its a good way to learn

Yes, it's ok as long as you don't move the pieces when you analyse the position.

What do you mean by "online"?  Do you mean Erik's special term for correspondence?  If so, no problem.  If live, it's cheating.  Think of it this way.  If you were playing OTB and whipped out a little magnetic set and started moving pieces around, don't you think your opponent would object.  I'll find the rule for you:

In Live Chess, no outside assistance OF ANY KIND is permitted

OK, that said, as long as you're not moving pieces around anywhere except in your head, I'm sure most would agree it's OK.  But technically according to the rules, it's not.  Sorry to be a killjoy...

Is it cheating if I visualise the board in my head and make moves on that board... keeping mental notes on how they turn out?

It sounds a bit... exactly the same!

No, it is not cheating at all to have the game set up on a physical board.  To be clear, though, it would be cheating if you moved the pieces around in any way that was not just a replica of the current game position.

Look I agree there's nothing wrong with doing it, but the rule is very clear:

In Live Chess, no outside assistance OF ANY KIND is permitted

How is it outside assistance? (I'm just curious why you think it is as I do not think it is.)

It's a board, it's outside of chess.com!

It's just weird.
I wouldn't call it cheating. Some people don't have the kind of mental visualisation skills that others do, and using real boards are a great help.
Sure, in an OTB tournament I wouldn't allow it either, but it's definitely not cheating. Only a crutch.
It's like writing down variations while playing blindfold (blindfold here meaning text based without a board, not actual blindfold over the eyes), and going over them, rereading them while taking notes, preparing for your next move.
I've done that multiple times. In fact, rereading and adding lines has made me thinking in a more relaxed way than just repeating the moves played in my head until a certain point.
If that's not cheating, and I'm convinced it's not, then this shouldn't be considered, either.

You have an alternate view of the board.  Look guys, I'm just the messenger here, OK?  If I start playing long live chess games here, of course I'm gonna use a board.  But the rule is inescapable no matter how silly we ALL think it is.

it is a conundrum of ethics. to use a second board in order to analyze a game is most definatly considered wrong (except in cases like the turn based games where they actually give you a button called "analyze" which causes a second board to pop up on which you can do just that). however, there is no way for them to tell if you are using one. i might suggest though, that learning to make calculations in you head would be much more valuable to you. there are many resources online to help with this.

I'd be more than happy if my bullet chess opponents try using a real board alongside while they play me!

Don't get defensive. I just want to know why you think that. Saying that you have an alternate view of the board is not an answer becasue in a live tournament I am alowed to walk around the board to get "alternate viiews". So getting an "alternate view" is not against the rules.

So what rule is inescapable?

As far as I am aware you can do all these while playing an over the board tournament, but you certainly can't get out your own board and start playing moves on it so I don't see why it is nonsense to be the same in live chess here!

Actually you have a real board in front of you already so it would be pointless.

@Olympian256:

Uh, no.  Even though we have some disagreement here as to the letter of the law, everyone here but you agrees that moving pieces around is flat out cheating.  Sorry, but your statement is wrong:

And yes , you can have a board and move the pieces around.

I also agree that it's NOT cheating. It's a great way to at least work your way up to a level of mental visualisation. Especially for those that can't play tons of OTB games for different reasons, to get them to a certain point in visualisation skills.
If that's cheating, then call me a cheater. Sometimes I even go to the toilet and take my trusty magnet board with me to try some lines while sitting there.

As long as you only replicate the position of the game and do not use it to play out candidate moves then it is perfectly fine. If it is "technically" against the rules then who cares? The rules are here to help us ensure a fair game. If a rule isn't necessary then break it.

Ignorant people aren't idiots. They're ignorant. See? Different words.