-I want to power the Nano with LM7805, drop by 7V is big
I'm going to use (on input and output) electrolytic capacitor 200uF and ceramic 100nF (saw it in some tutorial for powering Arduino).
-I'm going to power arduino through +5V pin. Some people say it's dangerous, because there is no regulator on it, but with protection on previous step it should be fine. Right?
-LED strips are going to be connected to +12V and theirs "-" to transistor to GND. Can and do I need to protect the circuit if someone provides +12V here? Like shortening the wires on LED strip?
-As per moving it from breadboard, like I said I tried Eagle free
The capacitors should be mounted physically-close to the leads, and its generally OK to use a larger capacitor. However, the type of capacitor is important. Electrolytic capacitors don't "act like" capacitors at high frequencies. So to prevent high-frequency oscillations/noise/instability you should use ceramic capacitors, and it's OK to parallel the ceramic with an electrolytic.Yes. Your 7805 should be fine.
@HellasT, are the values of the capacitors coming from experience?
@HellasT, this may be standard, but if that would be 7809, would the values be different? I suppose that other devices drawing power from that 12V will influence this.