The both of you did very well. A couple of things are wrong, or at least slightly incorrect, but, overall, that is the gist of it. We'll get into more detail on the genjutsu, and, through that, I'll try to correct you.
Okay, so, in my opinion, the most important aspect when fighting with and against Genjutsu, is know the limitations of it. Basically, what it can affect, what it can't. What it could affect, but the description that came with it, when your opponent used, was very poor. And, in essence, is knowing what is real and what is not, when inside a Genjutsu. I call this: Recognizance. You need to master the reality first, in order to better recreate it with a Genjutsu. And, by knowing the weak spots of a Genjutsu, where it's too recognizable, or where reality crosses with the illusion, you're able to better adapt to the genjutsu, making your techniques stronger.
You already said that recognizing you're in a genjutsu is important, but I need to put emphasis on this. It is crucial that you're able to understand and reason yourself that you're in a genjutsu, otherwise you won't be able to use a counter for it. Breaking out of a Genjutsu just because you know you're in a genjutsu, because you can read your opponent's move, is godmodding, and is not allowed. Likewise, any reasoning you do, it must be done fast. Especially on a fast-paced fight, if you go on long discourses about how you know it's a genjutsu, it makes it unrealistic and not a very good counter (And could even mean your loss). Without further ado, here are a few pointers:
Obviously, the easiest way to figure out you're in a genjutsu is about how bizarre a certain situation is, either because it's too fast or unrealistic, or because you can't pinpoint how it began, or even because it's working in a way it isn't supposed to. Something like the sky suddenly turning red, or things starting to move around or distort, usually means a genjutsu (Hallucinogenic structures may appear to be a genjutsu when they're actually not, so you need to figure out right away if you're fightning with a Biological Warfare type of ninja).
That is the second way of realizing you're in a genjutsu, when you know the ninja or know enough to understand that whatever the genjutsu is creating is beyond the capability of your opponent. For example, if you see a byakugan user create a tree. You have enough understanding of RP to know that these KG don't match. Beware of KG that do match (Mostly elemental KG). This is also the case of people create genjutsus of animals that they cannot summon. Except Pein, a ninja can only summon one animal type, so if someone you don't know summons an animal, and then creates a genjutsu of a different animal, you can pretty much assume you're in a genjutsu. Again, Pein did show the ability to summon various animals (And so did Nagato by himself), generally attributed to the Rinnegan, but I know for personal experience that there aren't others, until it happens, I'll teach differently. Of course, you need to keep doubting and experimenting, new combinations happen all the time.
Of course, if you do not know the ninja you're fighting, you have to assume some hidden skills, and learn what is real and what is not by trial and error. (And this is why it's crucial to be informed)
Other than Bizarre Effects or Unattained Skills, you need to rely on the genjutsu's own limitation. Especially in lower ranks, a genjutsu will only alter a couple of basic senses. Sometimes, a genjutsu can be purely visual, so, sounds associated with what the illusion is creating won't be produced, and you can use that to your advantage. Other times, you can see some light changes or superposition of images (for example, you may see an illusionary animal or clone that doesn't bend grass when it walks). You can see a tree constricting you but not hear it grow. etc etc. When a genjutsu breaks the B rank mark, it starts to complexify, especially in the hands of a good genjutsu user, and start to describe a richer experience, but even masters make mistakes, and even powerful genjutsus have limitations, you just need to explore them.
But as you fight, you'll start to get experience in seeing genjutsus and what to expect of them. Good?