Salut Definitelynotsane,
I'm a little bit lost in your post so I go by the way how I do it hoping it will help plus trying to answer some of your questions.
I'm not sure what do you mean by "fruit kvass" I assume a beverage which has a fruity flavour when consumed or something like ginger beer etc, right? I'm not sure about the vegetable brines as starters, I assume they may do, I do personally kombucha, water kefir and kefir whey based beverages. Naturally you can flavour all of them, I would recommend to do so by the end of the primary fermentation before bottling. If you do it too early you may get off flavours coming from the microbes breaking down the ingredients plus mold infecting the floating parts. However be aware of materials high on sugar like juices, syrups and fruits because they can easily turn into bombs, these you should add sooner but than alcohol may be created. Concerning that vomit smell of the fruits on the top of water kefir you mentioned, well I have a bad news for you, that is kind of normal. People not used to these ferments complain about this type of odour on regular bases and there is not too much to do about that I'm afraid, other than add some ingredient to cover it. I had some water kefir cultures which smelled fine but that is a long time ago and kefir based ferments are no better - sulphuric compounds from the milk so you can choose vomit or rotten egg, be my guest
If you want to do ginger beer, I do these days for batches of 10 l - 6% (w/v, 600 g) of light brown sugar, water kefir culture 2-3 l (grains) or 1% (v/v, 100 ml) of milk kefir whey, ferment for one to two weeks (milk kefir takes around a week) based on temperature. When it tastes to your liking strain the liquid and prepare a new culture and to the harvested beverage/base add around 2% (w/v, 200 g) of freshly grated ginger plus 0.5% (w/v, 50 g) of freshly grated curcuma, cold infusion for one to two days. After that strain the liquid and bottle. Secondary fermentation two to three days should do (20-30°C) but again it depends on temperature. If you would like to be super cool you can add for the cold infusion also some zest of citrus based fruits (mandarine is lovely) but be aware you may have harder time to get your drinks fizzy after that - it may be the essential oils interfering, therefore adding also juice of that fruit may help to over come this.
Anyway I hope it helps, best of luck and enjoy!
Sincerely,
Frantisek
PS If you add the ginger at the beginning of the fermentation it may affect the microbes - I would say they would go over it but they may not be super happy. Also keep in mind that ginger has by itself some yeast cultures directly present in it's inner tissue, not sure to what degree they would be active in the fermentation thou ...