Two bugs, I think, in the Android version of YGO PRO. Yes, 1.3.3, the latest version. Device is the Kindle Fire HDX thing, I think.

Anyway, Spellbinding Circle seems to have trouble knowing when to leave the field. I was playing the Yugi AI I think, and he equipped it to my Paladin of Photon Dragon. I activated its effect, sending it to my graveyard to bring out my Galaxy-Eyes Photon Dragon, yet Spellbinding Circle remained, even though PoPD was in the graveyard. It wasn't equipped to my GEPD either, so it was just there doing nothing.

For the Kaiba AI, he can evidently use the second effect of Enemy Controller to take a monster, but doesn't tribute any of his (maybe he didn't have any played and that's why he got away with it; I'm not sure if he had monsters in the field or not at the time). I've had this happen to me like three times far. I tried the card but had to tribute a monster...perhaps there's a way players can exploit the card, though?
For Spellbinding Circle; it did not leave the field because you sent the equipped monster to the graveyard. Spellbinding Circle only gets destroyed if the monster is destroyed.

As for your second problem; "ScrewTheRulesIHaveMoney.jpg"
I'm pretty sure it is a bug with AI in general. The Ai can be a bit buggy with cards that use tributes for a cost.
Mm, I see. I thought it was a bug, cus, having it there just taking up room doing nothing seemed dumb, but what you said makes sense. Glad Enemy Controlller's bug is AI-related, players exploiting that would be very annoying. Anyway thanks!