Let's go line by line.
- that death does not alter the structure irrepairably
As far as we can tell, if we freeze it quick enough, it won't. No magic required. (death doesn't mean something magical is happening to matter, it only means molecular machines stop working the way they should)
- that the structure and information contained therein will not degrade over time
Possible. Manageable with technology. Testable. No magic required.
- that the freezing process itself won't damage the information
Possible. Subject to fixing by improved technology. Testable. No magic required.
- that the information will be recoverable
Possible by definition of solving previous two points. Subject to advanced enough technology, which cryopreserved people are hedging against. No magic required.
- that we will be able to make sense of such information
See above.
- that the information after successful restoration can be transplanted into some other medium
Not required. Technology advanced enough to revive a cryopreserved patient will likely be able to fix the original medium. Technology already exists (in form of nanotechnology - viruses, bacteria, proteins, enzymes), but we don't know how to use it yet, as we didn't build it. No magic required.
- that this other medium will be able to 'execute' using that information
See above. Also, if you really insist on another medium, then it depends on whether or not brains run on magic. If they are not, then the problem is addressable with technology (develop a good enough medium).
- that the electrical component of brain activity once lost can be restored
Evidence suggests that this component is mostly irrelevant. Even if, it's solvable with technology (tough luck to those already preserved though). No magic required.
- and that all of the above will result in a restoration of consciousness
Unless you believe consciousness is magic, it's possible by definition of solving #2/#3.
- and that this consciousness will somehow be given the status of person (that's more of a social issue)
That's a social issue, but again, if consciousness is not a magical process, we can hope the society will mature enough to be able to accept revived people as persons.
> All of these together to me are equivalent to or maybe even greater than believing in God.
Now this IMO does not follow. There're no supernatural phenomena required to address any assumptions you stated, so isn't this by definition requiring qualitatively less faith than religion?