The second question can be answered with yes in most of the cases. Which gain setting do you have?
Did you install the graphs1090 script, so you can monitor your message rate? There is one indicator regrading the “noise” level. With ths you can find the gain setting.
If you reduce the gain too much, it might work, but will have an impact to your range. In this case you might need a filter too, depending on your location.
You can read more about it in the link below
For the MLAT question, you might need to wait for the experts here-
This is the page for the graphs:
And a longer discussion about filtering