Highlighting dated cells

I have a spreadsheet where a date is entered into cell C6. I need the cell formatted to highlight red if the date is 1 month or more in the past. Would I use conditional formatting for this, if so, what formula should I use?

Secondly, I need adjacent cells to highlight if the date in them is one month or more after the date in the previous cell.

I have attached a copy of the spreadsheet to show what I need the end result to look like.

Thanks in advance for all help and suggestions.