I’ve recently purchased a 2005, 350z with 177k kms
fresh service one month ago, all new fluids etc.
after one month of driving oil has used a quarter almost half of the oil in it.

There’s traces of oil around the dip stick and etc.

 

Welcome- your question and attached pics don't really yield any answers on oil consumption. It's unlikely you' lost that much oil past the dipstick. But you could have excessive piston ring wear or possibly valves. If you're that concerned, have a technician do a leak down or compression tests to determine overall engine condition. It's why I recommend all novice car buyers PAY for a mechanical assessment from a Nissan tech prior to buying a used car.