Learn English – ‘Sometimes’ & ‘However’ at the beginning or in the middle of sentences

Short answer

• Once can function as an adverb, adjective, conjunction or noun
• Since yes, can also function as adverb. Since can also function as a conjunction or preposition
• After can function as a preposition, adverb, adjective noun and conjunction

Long answer

You are correct in the overlap between once and since, they can both function as adverbs and conjunctions.

Adverb

• [Once I made] a cake from meat or [I once made] a cake from meat - once is the adverb describing the verb 'to make'. The description is that it was made in the past tense, hence the past participle usage of 'to make'. Once describes a single isolated instance in the past.
• [Since I made] a cake from meat I felt ill or I made a cake from meat and have been feeling ill [since I made it] - since is the adverb describing the verb 'to make'. Since can link the past to the present, implying that you still feel ill

Note that since is the adverb of the verb "to make", but in the sentence "I made a cake from meat and have been feeling ill since I made the cake from meat" there are a lot of unnecessary duplicate words. This can be shortened to "ever since", "ever since then", "since then", "since that time". However, the word still functions as an adverb of made, linking that time with now. The phrase "I since made a cake" is not used because there is no way to link then and now. You need to say "since the time I made a cake from meat" - "I felt ill".

Conjunction

• Call me [once] you get there - same as above, linking the phrases in a finite sense.
• He has been calling me [since] he got there - same as above, linking the phrases in a continuous sense. He has called me and he is still trying calling me.

Preposition

This indicates a spatial, temporal, or other relationship. Since and After can both be used to indicate a temporal location.

• Since that time, since yesterday, since breakfast
• After that time, after tomorrow, after lunch

Again, since implies a past event that is still continuing and as such is often used with the Past, present and future perfect continuous tenses

Once however, does not really get used as a preposition because another preposition is often inserted to be more specific. For example, the prepositions are in bold:

• Once upon a time
• Once in my life
• Once on the planet earth

So to conclude, there are similarities between once and since, both describe time but once is finite and since is continuous.

I always thought of after as a straight forward preposition but looking at the dictionary definition it is indeed quite versatile and can be used as an adverb as well. "After I made the cake I felt ill". In this context it would mean "immediately after".

Firstly, let's tackle the use of the phrase "you know everything there is to know about me" and ignore the word "else" for now.

It would be equally grammatically correct (and not really change the meaning, either), to say "you know everything about me." In this context "there is" is basically synonymous with "that exists."

You know everything [that exists] to know about me.

So, reworded, this means of all the things there are to know about me, you know every single one. This is obviously the same meaning as just saying you know everything about me. It is, however, a slightly more emphatic way of saying it. Generally the more words you use to express the same meaning the more emphatic you'll sound. So "you already know every tiny little thing there is to know about me" sounds even more emphasized (and, in this context, more aggressive, too).

So the other half of your confusion seemed to come from the word "else." "Else" needs to refer to something, and in the specific context of this sentence, ought to refer to the only thing the listener didn't already know (or still doesn't). It's easier to see why it's being used when the thing it's referring to is in the previous sentence.

I'll leave you instructions on how to prepare the side-dish, but you know everything else [about preparing this meal].

Here the "else" is all the meal preparation other than the side-dish.

Do you really not know my favorite color? How is that possible? You know everything else there is to know about me!

Here the "else" is everything about the speaker other their favorite color -- which brings us back to the context you provided.

Without knowing exactly how the conversation went prior to this sentence and only having the vague context it's a little hard to say exactly what the "else" is referring to. It sounds like she may have just asked him a question, such as "Would you like some sugar in your tea?" or perhaps "Why are you upset?" and he responded with this, meaning she already knows all facts about him other than this, and thereby implying she should probably also know whether he takes sugar or why he's upset. There is a little wiggle room here since he's obviously being sarcastic and refusing to come out and say what he actually thinks, so he may even be referring to everything other than the fact that he doesn't like horse racing.

Regardless of the words he picked, what he's actually saying is, "You are acting like you know more about me than you actually do, and I want you to realize that."