No, you use satellites for communication, not for wallet storage. Your PC/phone currently send and receive block transactions only from the Internet where nodes continually agree by consensus on the blocklist state. A satellite communication channel would  be the new way to communicate with nodes that does NOT route through the Internet.  The satellite itself could indeed be a node, but it would also work as a mere communication channel between Earth based nodes. Making the satellite a node would require more work, since indeed it basically needs to be a PC powerful enough to hash-check transactions and such. Not sure if the significant added complexity and wattage of that would offset the communication savings.

Yes, small sats like these have lifetimes measured in years, maybe not even 10 years. That's why you launch hundreds (or thousands?) at once, and then periodically to keep them "in stock".