1) If I burn a new USB every now and then (how often?) with the latest versions of a distribution, is this sort of equivalent to
a full install with subsequent periodic updates/upgrades, What do I miss with this approach (don't care much about
speed)?
How long do today's USB sticks physically last with a moderate volume of read/write cycles? If I actively create
data during a session I can move them to a location managed by the OS that runs on that computer, e.g. Windows,
which the life-Linux session can access. But how can I minimize behind-the-scenes r/w OS activities during a session?

2) It seems that 32-bit versions are disappearing from many distros, so maybe I am fighting windmills when trying
to keep an old, but good laptop alive via Linux. Is that the case?

Live CDs/DVDs (not life) are volatile by default i.e. the system runs completely from RAM and any changes are lost when its powered off. There are a few ways to create a live version with persistence. You can install a full version but how long it lasts depends on how often you write but that can be minimized with a few changes to the filesystem options. If I remember correctly one member used a full install and the drive lasted a few years but it depends. A new live version would be a equivalent to a new install and you could copy settings if you saved them to a different drive. How often just depends on the distribution's release cycle of choice.

There is still a number of 32 bit versions around but yes how much longer a distribution supports the x86 architecture is anyone's guess.

Cut down on the writes to disk, with things like noatime, etc.

Save files elsewhere, internal disk, another pendrive, keep a back up pendrive containing all your personal files, & it should work/last for a long time.

Regarding 32bit Linux, it is being phased out, however there are alternative O/S that still consider 32bit a viable system, the BSDs & Haiku will likely be the new alternatives.