Audrey,
I recommend reviewing the Marketo Sync documents.
You should NOT set Lead Score in SFDC. That is for Marketo to change, this is why it is overwritten.
Pretty much any field on the Lead or Contact can be written to by Marketo. The way to avoid this is to tell Marketo to block certain fields if they already have data. This is called Field Blocking. Usually you want to block Lead Source and contact details.
Read my documentation here: http://www.marketingrockstarguides.com/marketing-rockstars-guide-to-marketo/
The Date Field - what date is this for and why is it supposed to be reset? It sounds like you want it to be NULL, so it is.
Lead Status sounds like it should be updated in SFDC, which is what it is doing. Marketo can also listen for this value as well as change it. Sounds like this is fine.
Essentially, Marketo does the following every 5 minutes or so:
-Did SFDC have a change on a field on a record? If so, sync the the records if they are in both systems.
-Do I have to push over new lead or was I asked to sync over data that I have? If so, update the SFDC records. This will overwrite some data.
You can also check your Marketo User to see if the user is seeing all of the fields you want it to see and has permission (or not) to update them.