This already exists. The problem with this that the magnetic strip basically only stores your credit card number. Faking swiping a card would be very easy to do.

Though this idea already exists, the thought of faking a swipping being done scares me. I have never really shopped online, but i like to be sure that my credit card number is safe, so what if the machine does not store it? A product for the machine to ask you if you would want to save the number or not. I think this would be better so that each one of us could have a bit of peace of mind.

This would not improve security.
The security problem is after the number leaves your computer. The server at the other end cannot tell how you entered the number into your computer. Since it is "your" computer and you can program it any way you like, a crook could re-program their computer to lie and claim a number was swiped in when it was really typed in.

My card has an extra 3-digit number on it, which is not on the magnetic stripe and which I must also type in for online purchases. The object is that a store who swipes my card does not know the extra digits, and so an employee who sees my card number when I swipe it cannot use this number for online purchases. This is better security.

You are always at risk whenever you use or even posess a line of credit. Paying with cash at a genuine store is overwhelmingly preferable in terms of security. Any form of human interface can be cracked and exploited. In a way, it is up to the credit companies to limit, rather than increase, the number of opportunities for a number to be used, or at least to secure their valid use through authentication. Traditionally this was through a signature on paper. Now it's been reduced to knowledge of a zip code or other (easily fetched) piece of info. Soon, mere possession of a magnetic number will be all that is required. Thus, recognizing when a particular charge is not consistent with someone's consumer habits is paramount.