In solidity, if a function reads state but does not modify any state, this needs to be declared as view function.
If a function does not read any state and also does not modify any state, this can be declared as pure function.
If a function modifies state in the blockchain, to invoke the method you need to make a transaction in the blockchain and sendTransaction is the api to do this.
estimateGas api provides the amount of gas to be incurred to access/modify in the blockchain.
In solidity, only making transaction will cost you gas. If you just directly call view/pure function, it will not cost you any gas.
Point to be noted that, if a view function is internally called inside a non view function, so this must be transaction as it is modifying state(non view function).
Any operation in the blockchain state will cost you gas in case of making transaction.
sendTransaction is only for sending ether, is not true. Sending ether/ updating any variable of a contract means changing in the state of blockchain. So this will be transaction and this will cost ether.
estimateGas is an api which gives the estimation of gas to be incurred if that method is called as a part of a transaction.
transactionReceipt is returned only when a transaction has been added in the blockchain after being mined. So, in case of invoking pure/view function, you will not get either transaction hash or receipt.
Obviously, if a function needs to receive ether at the time of transaction, only then you will add payable modifier to the function.
Hope it will help you to understand the concept of transaction in ethereum blockchain.
For further information, go through the documentation of solidity.