I created a CoinBase bitcoin wallet address, can I share this address with Electrum desktop software instead of having different addresses and paying the transfer fees. Or is there another wallet like coinbase that has less fees and good security. Bear with me, I am new.
I created a CoinBase bitcoin wallet address, can I share this address with Electrum desktop software instead of having different addresses and paying the transfer fees.
No, because afaik Coinbase does not provide access to the private keys for this address, and so you will not be able to control this address from any other wallet software. In order to send a transaction from your Coinbase wallet, you will have to submit a request to Coinbase to initiate a transaction, and then their service will (hopefully) craft and publish the transaction for you. The point here is that you can contrast this custodial wallet model with a self-sovereign wallet model, in which the user is fully responsible for maintaining their own private keys (funds). (disclaimer: I have never used Coinbase, but it is my understanding they are a custodial service, and in that case the above is true).
In order to spend some bitcoin, you need the private key for the bitcoin address in question. If you use some wallet software that is non-custodial, the software will create and manage these private keys for you in the background (a bitcoin address will be presented to you). If you so desire, you can import the keys to another wallet, so that you can spend your funds from one of several wallet instances. Many wallets these days are 'hierarchical deterministic' (HD) wallets, which will provide you with a 12 or 24 word 'seed phrase', this seed phrase can similarly be used to recreate an entire wallet on a separate device.
However, in general, having multiple instances of the same wallet is not the most secure method of using Bitcoin, as you would now have a larger possible attack surface. If any one of your wallet instances is compromised, then your funds could be stolen. Additionally, entering private keys into software is a moment of vulnerability, as a keylogger could be present on your machine, waiting to grab any bitcoin private keys, etc.
Many users will instead create several wallets, using various software and with varying levels of security between them. Maybe one wallet holds the majority of your funds in a super-secure manner, while another wallet is easily accessible through your mobiles phone, with a small amount of BTC on it for day-to-day spending, etc.
If you use good wallet software and are cognizant of the mempool backlog, you can send non-time-sensitive bitcoin transactions for extremely cheap. If Coinbase is offering cheaper fees than what you would actually pay to miners otherwise, then that probably just means they are making money off your use of their service otherwise. Generally I would not recommend using them as your wallet, it is a better idea to educate yourself on how to use bitcoin to regain monetary sovereignty, not sacrifice it to some corporation.