Your problem is not very clear. You want suggestions about how to create cards in a way that shows the relationships between words? I will tell you what I do.
To show related words, you can color code cards (for example, create a Note with a green background for masculine nouns and a red Note for feminine nouns), add some kind of textual mark to notes, or even add sound files to Notes (the sound of rain for feminine nouns, for example).
If you have a Note for verbs, add a field for adjectives; if there’s no related adjective for a certain verb, just leave the field blank. Put both the verb and the adjective on the card even if they are the same; seeing them both is how you’ll remember that they are the same.
I find that synonymes are not very important in the early stages of language learning and take too much effort to learn if they are just a list of words (rather than something you learn in context; the context makes them easier to remember). I do add them to some cards, but I style the cards so that the synonymes are in a small font and located at the edge of the card, so they don’t take focus away from the important information (the new word and its definition).
On study days when I have more time/energy/focus, I might look at the synonymes. When I’ve reviewed the word many times and don’t need to focus so much on the meaning, I might look at the synonymes. Otherwise, I don’t usually do much with the synonymes. When I have multiple decks for a single language, I sometimes add the target word to one deck and the synonym to another deck for the same language, and study them as individual words.
Compound terms: let’s say you have ‘blat’ and ‘blat sprat.’ If you don’t know what ‘blat’ means, maybe just don’t add ‘blat sprat’ to the deck until later, or add ‘blat’, then add a bunch of other new cards before adding ‘blat sprat’ so that you have time to learn ‘blat’ before Anki shows you ‘blat sprat’ (this works only if you learn new cards in the order you added them). If both terms are already in your deck and you fail ‘blat,’ just suspend ‘blat sprat’ until you are ready for it. Or go ahead and review ‘blat sprat’ anyway; you might find that it helps you remember what ‘blat’ means.
I think that learning expressions with Anki is a bad idea unless the expressions are part of your native language. The more words you have on a card, the more difficult the learning process.
However, one method is to split the expression up; create cards for every word in the expression. Use the expression as a sort of example sentence on every one of those cards. Then you can focus on learning the individual words, which you have to do before you can learn the expression; however, you’ll have a second layer of learning: seeing the expression many times because it’s on multiple cards. However, the individual words should be the main focus.
You might ask yourself if you really need to learn all these different aspects of the language. Maybe some of these things will come naturally as you improve basic comprehension of the language (with individual words). Maybe some of these things are better to learn at a more advanced stage. Maybe some are better learned with a tool other than Anki, and some are better learned with separate Anki decks rather than tons of info packed onto individual Notes.