Yes, that basically covers most of it.
It's good that you know that Kai can only protect against B-ranked and below genjutsus, as people may often mistaken that fact as in the anime/manga people were able to break free from an A-ranked.
Also remember if put under a genjutsu you have to explain why you belive it's a genjutsu and so on. You cannot say ''As you put me under the illusion I use Kai'', you have to explain how you know you're put under the genjutsu.
It can be usefull to have a shadow clone by your side if you're fightning a genjutsu user as it would probably notice that you may not follow up on your tactics and realize you may have been put under a genjutsu. They can break you free from the genjutsu by simply laying their palms on you and channel their chakra into your body which would flust out the opponents.
If you're put under a genjutsu which could be a high-ranked genjutsu where Kai wouldn't work and you don't have any shadow clones nearby, you can bring pain to yourself as said. However it have to be good pain, like stabbing yourself with a kunai. Biting your finger or your lip wouldn't be enough.
Also there are other ways of breaking through genjutsus like Chidori Nagashi as when using it, it will surge throughout your chakra system and release you from B-ranked jutsus and below. Jutsus that work like Chidori Nagashi can only break one rank below their own, meaning that Nagashi can only break B-ranked as it's A-ranked. If you used one that was S-ranked it would release you from A-ranked. For S-ranked jutsus you have to bring pain on yourself as there isn't any other way, unless you have for example, Sage Mode which gathers Natural Energy which protects you from all genjutsus besides genjutsus on same level as the Mangekyou Sharingan(Sorry my spelling.

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Now that I have explained most of what you said, just in detail, I will be teaching you Kai, in other words, release. Kai works by stopping your chakra flow for a moment and then releasing it again in somewhat of a burst which clears your chakra system from the opponent's chakra.
So I will be putting you in a genjutsu whenever you're ready and we will see if you're able to break it. Though if any questions, please do ask as I do only want to help.