Tencent tends to tax the CPU and rely less on the GPU, you can give it a go as is and see if you can achieve any form of play-ability but I'd doubt that will be a success. For PUBG, I'd ask you to look at getting a system/platform that is a little above minimum system requirements for that game.
the right 710, yes.
the GX620 was available in several sizes, from mini to towers PCs. you will need a low profile card with a half height bracket to fit in ALL of them.
only the tower model can handle a full sized full height card.
the gt 710 get power from the slot so the PSU will not be an issue in any of the case sizes available.