There are several ways you could do this. You could create your own copy of partials for the component instance by putting them in the theme. See: https://octobercms.com/docs/cms/components#overriding-partials
I do not understand how you are trying to filter, so I can not help much there.
The "MyEvents" page variable is an array keyed by [Y][M][D][ Sequence ]. You can see it's format at the bottom of the documentation page here in market.
To learn more, you can look at the partials and code in the public repo.