Does a single speeding ticket (Drove 38 kmh in a 30 zone) and a parking fine affect NE application?
Driving 8km/h too fast in town is only a Ordnungswidrigkeit (misbehaviour), wrong parking, too.
They don't affect the Niederlassungserlaubnis application.
It is affected as soon a Verkehrsstraftat ("traffic crime") is involved. Some things which may be considered a Verkehrsstraftat by a judge are for example driving without license, driving while on drugs, hit&run, and failure to render assistance. Driving way too fast, or driving slightly too fast and causing a crash, or driving carelessly and causing a crash can also be considered a Verkehrsstraftat.