So, I just heard of the altcoin called 'Bitcoin XT' and it is forked from bitcoin. I want to ask that, if I make a tx from the core chain or xt chain, will the tx be added to the another chain? Does my balance in core chain the same as in xt chain?
Both chains being active at the same time is a bit of a disaster. If you have existing coins (e.g. cold storage) that you don't move, those coins are fine on both chains.
How about if I received bitcoins from someone using XT chain? Will the tx shown up in core chain and blockchain.info? And vise versa?
Not necessarily. As I said, it is a bit of a disaster.
If the transaction has a coin history including only old, pre-fork coins, then it is valid on both chains, but won't confirm both chains at the same time, so it could be double-spent on one chain and not the other.
Transactions that have a coin history including coins mined post-fork will be valid only on one chain.
For this to not be chaos one chain has to die quickly.