We want to make changes to Mom's Medicare plan, if I research options now will the pricing be the same in October during open enrollment?

I would do research now, narrowing down the choice(s) to some good candidate plans, then double check rates when open enrollment occurs. That way you'll have made your short list of plans and only have to compare rates in a few months.

The Medigap plans we chose weren't at the time subject to open enrollment, so we signed up as soon as I did my research and decided which ones we wanted.

BTW, I used an Excel spreadsheet to create a database of comparison factors for easy reference.