Taxes after separation
A joint tax declaration is always better, as it leads to a reduced tax rate. It can be still made for the year of separation, even if the separation took place in the beginning of the year. A joint tax declaration is especially advisable, if the taxes were paid on the basis of Lohnsteuerklasse (LSK) III and V. The spouses have to agree on a joint tax declaration and it is possible to sue the other spouse for his agreement to it.
In the year following the separation the taxes are calculated in the same way as for unwed people. That also means that the LSK needs to be changed to I or at least to IV (or II, if you take care of minors). This is especially important, if you have been taxed with LSK III during the separation year.
For better understanding: The LSK III/V reflect the possible result of a joint tax declaration of spouses not living in separation at the beginning of the year.
Taxes automatically deducted monthly from your work income are just advance payments to the state tax agency (Finanzamt), on the assumption that the yearly income will be the monthly income, multiplied by 12. So you always should declare taxes (Einkommensteuererklärung), if you haven´t worked all year, as you get some (or a lot) of the advance payments back.