Your exterior walls?
yes you can
Cheryl A: those are lovely - but they're not parquet wood floors (which I put down on my floors back in 1976 - and which lasted till 2003 when I couldn't WAIT to rip them up and out to replace with stone). :) If they're asking about typical parquet wood flooring (small strips making up 4 6" squares at right angles to each other comprising 1 foot squares) - personally I think they'd look terrible on a wall, and would probably be difficult to affix since they're quite heavy (the Bruce and Hartco ones I used needed to be put down with a below-grade mastic--very messy stuff). IF, the idea is to use long strips as shown in your links and then butt them at right angles to each other in 2-3-4 foot sections - it would make all the difference (and using white, cream or greyed/ash coloured flooring) would look really good, and modern.
Wood parquet can’t be used on the exterior, even if it has been sealed with exterior grade polyurethane, because it has no drip edge and has no exterior grade backing.
Yes, on the inside.
Are you sure it is parquet that you are referring to, or something else?
Examples below show what wood parquet interior flooring looks like: