If it connects with no encryption it does support the channels (as I'd expect it to - China and Japan have enough channels in common with Europe).
(You used to have to avoid channels 12 and 13 with much older USA devices if their driver could not operate in a world-wide mode. These days chipsets in infrastructure station (client) mode are meant to defer to accepting channels from the country reg. code set on the AP. They might still be restricted only when operating in AP or ad-hoc mode)
That said, stick to 1-13 on 2.4GHz and 36-48 on 5GHz to be on the safe side. It looks like China does not normally use channels 100-144.
If you have had it connected to the same SSID without encryption you'll need to do "forget network" on the phone after changing back to encrypted on the router(s).
For your encrypted settings you should indeed be only using a WPA2-AES(-CCMP) PSK as that has accelerated performance on the Wi-Fi chipsets.
Avoid any options to fallback to WPA1 or TKIP.
Any new devices wanting to use the Wi-Fi symbol (trademark) since March 2006 have had to pass WPA2 certification so that isn't an issue here in 2020.
I would test setting a very simple passphrase consisting of only numbers to prove there isn't something weird like character encoding affecting the passphrase entry on phone.
Oh and on both routers will need to match passphrase where you use the same SSID
(which you can use on both channels - client devices can then pick whichever band is better which will vary with range and obstacles. If you use different SSIDs in the same location, Android phones will prefer the last SSID you connected to even if the other is stronger. Likewise laptops will have an order of preferred networks that could leave you connected to a weaker network if you move around).
If your second router is just acting as an AP for the same network this will be ok. If the second router presents its own subnet behind the first router, the SSID will need to be different as a hint to the client that it would be connecting to a different network in the same location.
prlzx on iDNET: FTTC (VDSL) at ~40Mbps / 10Mbps
with IP4/6 (no v6? - not true Internet)