You are having problems with your video capture device (Avermedia).
04:14:15.858: [DShow Device: 'Video Capture Device 2'] settings updated:
04:14:15.858: video device: AVerMedia C875 Capture
04:14:15.858: video path: \\?\usb#vid_07ca&pid_0875#201530700384#{65e8773d-8f56-11d0-a3b9-00a0c9223196}\{957bd672-7934-4b55-b81a-3e22b14c679a}
04:14:15.858: resolution: 720x480
04:14:15.858: fps: 59.94 (interval: 166833)
04:14:15.858: format: H264
04:14:15.906: using video device audio: yes
04:14:15.907: sample rate: 48000
04:14:15.907: channels: 2
04:14:15.907: audio type: Capture
04:14:16.449: error: non-existing PPS 0 referenced
04:14:16.449: error: decode_slice_header error
04:14:16.450: error: no frame!
04:14:16.450: Error decoding video
04:14:16.576: warning: Multiple frames in a packet.
04:14:16.582: error: non-existing PPS 0 referenced
04:14:16.583: error: decode_slice_header error
I have the same C875 but I don't bother using it for live streaming. I also happen to own an Elgato HD 60 (USB) and Elgato HD 60 Pro (PCIe+HDMI) as well.
I would never use the C875 to do live streaming at 1080p resolutions. I know that when I do game recording at 1080p on games like Call of Duty, the output looks like crap. You are better off buying a PCIe capture card like the Elgato HD 60 Pro or Avermedia Live Gamer HD 2 that does full 1080@60fps. Also, as you probably already know, the Avermedia C875 is only capable of doing up to 1080@30fps. You don't want to use that card for 30fps on high end animation games. It will look choppy, pixelated, if not stuttery.
In the main mixer, click on the wheel for your Avermedia capture card. It should be set to default. If it set to a custom resolution set (720x480?) change it back to default. Why is this set it to 720x480 and 59.94 FPS?
Let OBS Studio use the settings in the Output category, which should be 1920x1080 (1080p) base to match the Avermedia and your monitor resolution and 1920x1080 (1080p) or 1280x720 (720p) to be streamed out. I think you may have mistakenly overrode the output settings. Also in the output category, set FPS to 30.
When you get your new PCIe card, set FPS to 60.
Also, realize you are trying to setup two difference configurations here. One is a dedicated PC streaming setup that to your XBox One. The other is you playing PC games on the same system.
You need to save those settings and tweak them for each configuration. Don't expect one set of settings to apply to both configuration.