Hi @Ardra and welcome to the Quick Community!
I can see from your screenshot that you’ve already checked the “Hide Select all” box. The reason it’s still showing is right in that checkbox’s label: it only takes effect “if the parameter has a default configured.” If your parameter doesn’t have a static default value set, QuickSight ignores the checkbox entirely. Go into your parameter settings (not the control, the parameter itself) and set a static default value. Once that’s saved, “Select all” will disappear from the dropdown.
For defaulting to the previous month automatically, the simplest approach that I have found is to add a column in your dataset query that outputs your normal YYYY/MM values for all months except the previous month or current month, which you label with a static string like “Previous Month” or “Current Month.” Then set that string as your parameter’s static default. Since the underlying data shifts with each dataset refresh, the control always lands on the correct month automatically. This also solves the first issue simultaneously, since you now have a static default configured.
Alternatively, you can set up a Dynamic Default Parameter with a small helper dataset that computes the previous month value via custom SQL. This community thread walks through the pattern. You’d schedule a SPICE refresh on that helper dataset so it stays current. It’s more overhead but useful if you don’t want to modify your source query.