Generally, the tenants are required to provide the landlords at least 30 days written notice to vacate. So if you're are providing only 2 weeks notice, then yes, it is fair for the landlord to keep the deposit because she has to find another tenant quickly and/or she will have loss of income. You may get "some" not "all" of your deposit back because landlords are allow to charge reasonable cleaning fees to get the property ready for the next tenant.
Regarding a letter to explain "all that has happen"... not neccessary, why? for what? ... all a tenant has to do is to provide is a written notice to vacate...tenants don't have to provide a reason...it is a courtesy but not a requirement.