Hi plant people, I am brand new to this hobby, and thought I would start by trying to grow some Basil plants. Got a pot of commercial basil from M&S yesterday and separated some of the plants, trying to maintain as much as possible of the roots, then transplanted them as follows:  
In the big glass it's tap water with about an inch of stem submerged, hoping it will root? Is this how cuttings work?  
In the little pots on the right 4 of the tiny plants, on the left 3 bigger ones, but the one closest to the centre is already leaning (no idea if that's bad or if I should do something about it). They all received a light dusting of Mycorrhizal Fungi when transplanted, to aid with root development.  
All the pots have plenty of drainage at the bottom.

  
Between the glass of cuttings and the black pots there are a couple of snake plants, I potted them in transparent plastic desert containers with holes at the bottom to make sure the soil dries out fully before I rewater them again, but they seem to be struggling, one has already lost a leaf which I pruned off, and I don't really know what to do to help them.

  
In the back in the propagation trays there are some Coleus seeds that just sprouted, they seem to be doing ok, although some of the tinies look a bit yellowish, no idea if I should worry about it.  


Additional info:  
Everything except the snake plants are in Westland general houseplant potting mix.  
The snakes are in Westland Succulent and cactus mix.  
The grow lights on each shelf are twin 10W Barrina T5s, on a 12 hour timer.  
I've yet to apply any plant food to anything.  
Their water is treated with 1.5ml of white vinegar per 400ml, because I live in a hard water area, and a drop of water conditioner to neutralize the chlorine from the tap water.  
The room is about 15-17 C , around 60-70% humidity (I live by the seaside)

I never managed to keep a plant alive before in my life, even managed to somehow kill cacti before, so literally any advice would be welcome 

Basil guidance plus general advice for a newbie please