In indirect speech, the tense is the one that would have been used in direct speech, and this is the same rule.
Yesterday you suddenly realised: "I love her!". "Love" is in the present, so it stays in that tense even when you report that thought: "Yesterday I suddenly realised that I loved her".
If the sentence had been "Mi subite eksciis, ke mi amis ŝin", it would mean: I suddenly realised that I had loved her. The thought you suddenly had would have been "Mi amis ŝin!".
Well, the -is form could be past simple, present perfect, or past perfect.
Esperanto does have an explicit past perfect (pluperfect) form: "estis ...-inta". For example, "Mi estis leginta la libron" (I had read the book).
But those compound tenses tend not to get used that much.
In "Mi subite eksciis, ke mi amis ŝin", it just gets interpreted as past perfect in English because you are talking about something that was in the past from a viewpoint in the past (which we use past perfect for).
You could even do future from the point of view of the future that way :) English doesn't even have a separate tense for that. ("Tomorrow I will realise that I will love her in in the future"?)
The verb "koni", which means "to know" in the sense of "to be acquainted with" is used in speaking of persons, languages, places, etc. "Koni" always has a direct object. It is never followed by "ke", "ĉu", "kiu", or any other interrogative word. "Scii" means "to know" in the sense of "to be aware," "to have knowledge." It is not used in speaking of persons.
[Footnote: "Koni" is equivalent to German "kennen", French "connaitre", Spanish "conocer", while "scii" is equivalent to German "wissen", French "savoir", Spanish "saber".]
While there is some overlap in where you can use them, in general you use scii for facts, and koni for people, objects, places, etc.