Select from & to dates from drop down menu & plot the chart between the values related to that specific time period only. Changing the month & year will change the values as well as plot a new chart.
Manually change the min/max points of the x-axis. Can type in whatever date you want to limit what you see
Use a PivotTable, and filter the X-axis to only see the dates you want
Use formulas linked to your dropdowns, which then generate list of dates between Start and End. Your date could then be created using either SUMIF or VLOOKUP formulas, depending on your data
When you say plot a new chart do you mean create a brand new chart? or just update values in existing chart? I also don't understand your point about changing year & month since you're already changing dates in from & to criteria. in any case here's a sample file.