Google-sheets – How to change the year if I want to use the same spread sheet we used last year

Ultimately, you need to do what you already predicted: adding a leading zero. The TEXT function will make that happen like this:

=TEXT(A2, "00")

I've created a formula that takes on the complete column, filter for empty cells, brings together the MONTH and DAY and SORTs the lot.

Formula

=SORT(ARRAYFORMULA(TEXT(MONTH(FILTER(A2:A;A2:A<>""));"00") & " - " 
 & TEXT(DAY(FILTER(A2:A;A2:A<>""));"00"));1;1)

Explained

Here's a break-down description of the formula:

1. The FILTER function will filter for all rows that have something.
2. The MONTH and DAY functions will extract the respective values from the date.
3. The TEXT function will convert the value from point 2 into a pre-formatted STRING.
4. The ARRAYFORMULA function will apply all the above to the complete column (skipping the header).
5. The SORT function will sort the result, given by the ARRAYFORMULA.

The SORT function allows for sorting. If you do that via a column sort, the entry of the ARRAYFORMULA is taken into account as well and gets re-positioned, causing mayhem.

Screenshot

Example

See example file I've created: sorting dates as text

Use the following formula, to keep track of the notes:

=ARRAYFORMULA(IFERROR(VLOOKUP(A2:A32,Sheet2!A:B,2,0), ""))

If you have more than one note per day, then you can expand the formula to cover more columns:

=ARRAYFORMULA(IFERROR(VLOOKUP(A2:A32,Sheet2!A:B,{2,3,4,5,6},0), ""))