That is an OLD lower-end CPU, optimized for lower thermal output therefore low performance, not the computationally demanding task of real-time video encoding.
I recommend monitoring hardware resource (CPU, GPU, RAM, Disk I/O, etc) utilization to see if your system is being maxed out with your settings
You can check the forums for OBS settings for under-powered systems. Exactly which GPU may make a difference in your scenario (Intel QuickSync vs NVENC.. maybe??). I'd expect streaming to work on that iMac, IF you keep your expectations low (no high resolution, high fps/bitrate, etc). Hopefully yours is a SSD, not HDD, model? And monitor and properly manage your RAM usage.
Syncing is something you, as operator of video compositing system [OBS in this case], is responsible for dealing with (see online videos on suggested methods for A/V syncing, I use a MP4 video for just this purpose, running on a tablet with camera and mic pointed at that... pick what works for you and your system). You are also responsible for adjusting the audio mixer when you have multiple audio sources at same time. The Quick Start guide at
https://obsproject.com/wiki/ will help
also for
Audio related, maybe these will help you
