Unable to answer "Do you have to pay to park here?" – Parking Lot – https://osm.org/way/115307735 via StreetComplete 57.2:

1時間無料。1000円以上消費で合計3時間無料。無料でなくても、値段は施設利用するかどうかで変わる。
Price depends on whether you buy something at the AEON supermarket. If you do, 3h free, ¥100/30min further. If not, 1h free. ¥100/25min further.

Attached photo(s):
https://westnordost.de/p/216890.jpg