Is it possible to have a failed Bitcoin transaction on the block chain? In Ethereum, a transaction may get out of gas but still being included in a block with a receipt status of failed. In Bitcion, will similar things happen?
No. Invalid transactions do not get included in blocks in Bitcoin.

There is also no receipt concept in Bitcoin. All nodes run full verification and check transactions against their own UTXO set when importing a block. Therefore any invalid transaction will also cause a block to be invalid as well.