Hi Yvonnie,
I’m sorry that you’re running into these issues, but I’ll be happy to help you out.
For the first issue with the highlighted day, can you verify that the “Timezone” setting under Settings > General is set to the correct timezone (using the location timezone instead of the UTC offset)?
Regarding the wrong month displaying on mobile, I tested this out locally, but I am not seeing October on my end. Can you tell me which OS & browser you were seeing this in so that I can test it out there? We do have some tutorial-style articles in our knowledgebase, but regarding this topic specifically, this could be related to a conflict with something else on your site, as I am not able to reproduce this locally and am not currently seeing other reports of a similar issue. You can test for this by running through the instructions here. Please make sure to have WP_DEBUG enabled during testing and copy/paste any errors that you see into your reply. If you don’t have a testing site, the free Duplicator or WP Staging plugins can help you get one set up.
Can you also share your full system info with me?
Thanks,
Jennifer