How can I rip audio CDs and normalize them at the same time?
Normalising, as such, is not really helpful when importing from commercial recordings, as the Mastering engineer will have already made sure the tracks are correctly normalised, whilst maintaining the relative levels between each component track.

The only way to truly level-match would be using compression &amp; limiting algorithms, which really ought to be left to a professional, &amp; is beyond the scope of Ask Different.

The way to do this at consumer-level is to use iTunes for playback [&amp; also would be by far the simplest for the initial ripping, as it is capable of all your bullet points] &amp; switch on Sound Check in Prefs > Playback.

This allows iTunes to measure the apparent loudness of each track or album &amp; automatically adjust the playback levels on the fly, enabling more comfortable listening without levels jumping around track to track.

This is done by a system known as ReplayGain
See 'Alternatives' at the end of that wiki page for a brief explanation of why normalisation &amp; recompression are not ideal solutions.

However, iTunes has traditionally done this on a per-track basis, not a per-album basis, which can make quiet tracks in the middle of an otherwise loud album jump out at you far too much.
This trait is reported to be fixed in recent versions, but once a track has been analysed, iTunes will not go back &amp; fix it later.

To get around this, you may need to employ something like iVolume which is capable of resetting the iTunes data, then recalibrating. It will also allow you to specify whether any album or compilation should get individual or global adjustment.
You can also manually tweak any individual track/album manually.