If everything works normally without TL-SG108E, than just capture dumps on your client to see, how you receive 4 IPv6-addresses, and contact your local tplink support to fix it.

No, you cannot repeat wireless network with EAP225-Outdoor. The only thing you can do is to change your not EAP225-Outdoor to EAP225-Outdoor and connect both these APs via MESH feature

No, you cannot use it as Bridge. Only as Access Point.

More or less all vendors are almost the same. TP-Link is #1 SOHO vendor, so it is a good brand, however, everyone has his own opinion. For example, I do not really like tplink high-cost devices,...

24V adapter is probably Passive PoE 24V, which will not work obv :) If it is 24V power adapter, then you will just burn out your device. Try to find any 802.3af adapter, or any PoE-switch also works...

Oh, man, sorry, it is v1. Then still it supports 802.3af, like TL-POE150S , but it doesn't support Passive PoE. 12v/1,5A is only dc power adapter from the package.