Can I replace a Shimano MF-Z012 (freewheel) with a MF-TZ510?

Both of these models are freewheels not cassettes. They are for the most part interchangeable. The only area of concern would be the size of the largest cog. Too large a difference from you original model may necessitate a longer or shorter chain. You may also need to make some small adjustments get the shifting optimized.