Hi Vuk,
If I understand your problem correctly, you need to press the "Insert" key to change the cursor behaviour between the "fat" cursor (that overwrites characters with the ones you type) and the "thin" cursor (that simply inserts new characters when you type). This is not really related to Spyder or Python, though; I believe any text editing software will present a similar behaviour regarding the "Insert" key.
Hope this helps,
Fabio