How to smooth audio spikes on audio tracks.

I have my audio track ready that I painfully recorded with my own vocals and a not very good microphone therefore I have spikes in the audio and other parts that are very low volume, so my question is:

Is there any function in Cubase 9 pro to improve the whole audio, to reduce the spikes and bring up the parts that are too low?
I tried to use Audio/Process/Normalize but that only seems to bring the spikes down as in so far as the volume of the whole thing is reduced, or am I wrong?

So is there a way to automatically fix low and high peaks? Sorry if this is a stupid question

Also, any good free tutorials out there on vocal production for beginners?

Thanks in advance.

That’s what compression does.
I would add a compressor on the insert to tame the peaks, and add a limiter after the compressor to raise the overall volume of the track.

No need to add a limiter after the compressor , just use the make-up setting to compensate.