The Date data type in Access is intended to store complete dates: it's an 8
byte floating point number, where the integer part represents the date as
the number of days relative to 30 Dec, 1899, and the decimal part represents
the time as a fraction of a day. In other words, it's not possible to store
only mm/yy in a date field.

If all you want is month and year, consider storing the month and the year
as separate integer fields (unless you want to store a text version of the
month name)

If you've got complete dates in the field, though, you can easily retrieve
by month and year using something like the following:

WHERE Format([DateEntry], "yyyymm") = 200402

Maybe; but there is no need. You can use a normal date (allowing date
calculations by using standard functions) and if you don't need the day,
set it to 1.

Most certainly. Create an expression in the query like

format(yourdatefield, "mm/yy")

and put appropriate criteria below.

If you don't care about the day, just save it as the first
of the month (e.g., 3/1/2004). Then use the Month and Year
functions to retrieve the parts you want. e.g.

MyDate = Month(Date) & "/" & Year(Date)

Results in MyDate = 3/2004