Okurigana is to help the reader know which reading of the character is being used. As such, okurigana only ever applies the the kun-reading of the characters.
When you're seeing something like
[先]{さき}に
に here is not okurigana. The に is not part of the reading of the character. It is the particle に applied to the noun さき. Also, you can think of さきに as something of a set phrase for a beginning student of Japanese--that's probably the reason they provided it for you.
Indeed for each character you need to sometimes learn multiple on-readings and kun-readings. This can seem daunting at first, but with practice reading, you will catch on and begin to build an intuition.
The okurigana helps you distinguish between different possible kun-readings for the same character. The characters you chose to highlight, in terms of the readings provided, don't shed much like on why you might need okurigana. So, here are some examples for clarification.
To give a notable example, consider 開く 開ける
開 generally means to open. On-yomi-wise (On-reading) it's very straight forward: かい. But it has four other possible readings.
- [開]{あ}く
- [開]{あ}ける
- [開]{ひら}ける
- [開]{ひら}く
The English translation for all of these is essentially "open".
I give this example because it's one that confused me and gave me many headaches when I was first learning Japanese. My thinking went this way, "I thought okurigana was supposed to help you figure out the readings, but here for a given okurigana there are still two possible readings for the unexpressed part of the reading. How do you figure this out!"
Well, the Japanese have super-powers. lol.
Not quite, but if you're a native speaker of English, there's a distinction that is made with every Japanese verb that is essential to bang into your head. Every verb is either transitive or intransitive. So, if you're reading a Japanese sentence, you should eventually intuit whether the Japanese is building toward a transitive or an intransitive sentence. Your clue for this can just be the particle を. This particle always (please read the label, restrictions and exceptions may apply) indicates a sentence that takes an object: hence a transitive sentence.
So here are the same verbs again.
- [開]{あ}く to open (intransitive)
- [開]{あ}ける to open (transitive)
- [開]{ひら}ける to open (intransitive) but often used in figuratively with meanings ranging from to cultivate to to be open minded. This one is pretty easy to spot because of its figurative uses even if you don't remember that it's intransitive.
- [開]{ひら}く to open (transitive)
Please don't ask why there are so many verbs for to open. There are slight nuances here that you will be able to learn to discern.
So, if you see the sentence.
ふたを開く
Uncover a lid. (ie. to open a jar with a lid or something like that).
the particle を there is the clue that the verb is being used transitively. So the reading for 開く is ひらく.
Incidentally, please don't ever rely on the English translation to determine transitivity of the Japanese. Often the English and Japanese will be at odds (mostly what's expressed intransitively in Japanese is expressed transitively in English).
WAIT!!!! I wasn't asking about transitive vs intransitve verbs. I was asking about okurigana.
Yes, I know. I gave perhaps one of the nastier examples here. But still, the okurigana reveals to a observant reader the underlying reading of the character.
More generally, the situation is a lot more straight forward.
For example
Here the okurigana facilitate knowing which reading to use with the character 行