I make cards for words that I want to learn, I don’t tend to have words in my decks that are too basic and I am sure I don’t need to review them, so no, no place for 男の子 there. The words I add to Anki consists of roughly two groups:
- new words I encounter that I don’t understand;
- new words I encounter that I do understand from kanji/context but want to make them into my active vocabulary;
but in case of the second group I don’t always stop to make a new card if I don’t feel like it, either because I don’t find the word useful enough to remember or because I just want to enjoy whatever I’m doing and not study at the time. So the word “男児” could find its way to my decks (it’s not there as of now though).
No 支配 in my collection either, because of the above reason (too common), so I can’t give you the real example, but let’s give it some thought 
There’s actually a couple of different ways I manage synonyms.
Let’s say you want to make a distinction between 支配する and 治める/統べる/束ねる, which all can mean “to rule”. Distinguishing 支配 from them would be very easy because it’s different part of speech. So while me definition for, for example, 治める could be “to rule”, for 支配 it would be “+する： to rule” (that’s also how I separate na-adjectives from i-adjectives, like: 清い “clean” 清らか “+な： clean”).
Although my actual definition for 支配 would more likely be something like “+する： to rule; +者： ruler”, which could help distinguishing it from synonyms that are nouns too, but for example don’t go with “者”… although the only one I can think of is 統治, which does create the form 統治者 too, so in this case it doesn’t help But we can make 支配 into “+する： to rule; to control; +者： ruler” and at this point it should already be enough to differentiate it from the other. Usually synonyms don’t have the exact same meaning.
But what about 治める and 統べる then (束ねる is different enough to omit here, although it also can mean “to rule”)? Well, their meaning is not exactly the same either, but let’s say you don’t care to focus on any different meaning of 治める, just ruling. So both words could have “to rule, to govern” as their definition, what I could do then is to just change the order. For example I would write “to rule, to govern” for 治める and “to govern, to rule” for 統べる. The kanji for 統 simply makes me think about government more than 治 does, so when I see “to govern” listed first, 統べる is more likely to come to my mind. It’s very subjective but it doesn’t matter - it works
But when everything fails and I’m just at a loss what to do, I would simply do that: 治める “to rule (not 統べる)”. Works too. I have a separate field named “synonyms” where I put them though, I don’t include them in the translation as I did here. The field shows only when I actually put something there. But I would rather differentiate synonyms by their nuances in meaning if possible (usually it is).
edit: Also, I don’t think it is a bad thing if you recall the synonyms as well during review, if I can recall the word I was being tested on too quick enough then I don’t see a problem (of course if the other answers I recall work too),
My template for words is actually a bit complicated and I use a lot of fields
Front:
- definition in my language (translation)
- synonyms (if any)
- tags (if any); I tag for example all katakana words, so I know I’m supposed to give a katakana answer - helps with synonyms too, actually); I also tag 四字熟語 or sometimes slang expressions
- link to weblio.jp entry for the word (only if I don’t have accent information in the card already - it just makes it easier for me to add it as I can click it before I even look at the word so weblio.jp will already be loaded when I give answer and I can quickly copy the accent from weblio)
Back:
- word/expression in Japanese
- reading in kana (doesn’t appear when the word is kana-only already)
- accent (sometimes I use grpahs from OJAD instead, when weblio doesn’t have the accent information, I prefer weblio everytime it does though)
- Japanese definition (from weblio.jp)
- again link to weblio.jp (appears only if I don’t have the Japanese definition yet)
- example sentences
Here are some “real-life” examples to visualize it:
I review words, collocations, idiomatic expressions etc. the same way. As for grammar, it’s something I’m not quite sure how exactly I should go about yet I use SRS for it since very recently. I wrote about it some more here. You have already seen this post apparently, but I don’t really have much to add at this moment.
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