Using Views and Date module in Drupal 7 - Limiting Filter Options
currently "date" module doesn't allow to satisfy this needs

I see two solutions for the first question:

1) Develop a custom module in order to create this type of interaction.

2) A quick and dirty alternative is to alter the dropdown content using JS, but a custom module would be miles better.

Sincerely I'll suggest the first one.

About the second question you could expose the day filter and populate it substituting the form filter with a custom one, for example hiding the original form filter with CSS (display:none) and adding some hand crafted links with the URL parameters on the views header area.

Good work!