Can i use one pair public and private key for all transactions? Can I use one pair public and private key for all transactions, digital signatures and wallet addresses?
In the other hand, I have a private key and want to sign all transactions and have a public key for broadcast. Can I do?

Is this way secure?
Each private key is associated with exactly one public key, which is associated with exactly one address.  So if you only want to use one private key, then you can only have one address.  This is "secure" in that it won't make it any easier for people to steal your money (barring a successful attack on ECDSA) but it is not so good for privacy, since people will have an easier time identifying your transactions as yours.

It is also possible to have one "master" private key or seed, from which many different "child" private keys are generated.  This is how an HD wallet works.  It is associated with a master public key, which can be used to identify your addresses and generate new ones, but as mentioned above, it would not be good for your privacy to actually make it public.