Hope this helps, a bit lengthy but...
You maybe can use mesh but if you want to achieve the same equivalent bar area to 12mm diameter H12 bars then you may need to look at the B type structural meshes, perhaps a B785 mesh? The rub here is that the bars are different sizes in each direction with different spacing.
Has the slab (maybe basement walls too) been designed as a two way spanning slab. Roughly meaning that all the edges of slab are fully supported all round so that the main reinforcement bars act in two directions perpendicular to each. If so, then you may need four layers of mesh (2 top + 2 bottom) as opposed to your 12mm diameter H12 loose bars top and bottom as the secondary bars in the mesh may be too small.
Although mesh can be great you can have a problem with “nesting” if using lots of layers. Were four sheets come together it’s difficult to lap them properly and keep the concrete “cover” to the reinforcement. You can get a flying end mesh but on a small project this can add to the cost, difficulty in sourcing and you may need to detail it up so it fits. Also think about how you reinforce the corners of the basement walls as you can get congestion here too.
Although mesh can be appealing if you have congested reinforcement it’s harder to compact the concrete properly and that can cause problems later on.
Perhaps have a look again at using loose bars. An H12 is not a bad bar, not too floppy and not too heavy. They come in various stock lengths, easy to source and price match. Also, if you run out you can nip to the stock holder and grab a few more. Any off cuts are great for garden stakes or using as dowels etc.
Once you get going with tying loose bars you’ll get along fine I’m sure. If you make a small mistake then all you need to do is remove the odd bar or two rather than sheets of mesh that you may have cut.
Just remember that when rebar is tied together it is very heavy so make sure it is properly braced and shuttering is supported.
Clay soil (say when you have cut down a tree) can exert a significant load on the walls of a basement. The soil can take a number of years to readjust to the new ground water conditions.
There are a good few ways of designing concrete basements / floor slabs. When you don’t have other buildings /sewers etc close by then broadly some key areas considered are;
strength (so it does not collapse), deflection (so it does not bend too much and damage other parts of the structure) cracking (to control water ingress and again damage to other components and finishes) and buoyancy / drainage... it’s not a boat so you don’t want it to float if the ground water rises.
When a floor slab is say simply supported at each end only and it is loaded from above you will get tension in the bottom of the slab. Steel is good for resisting tension hence your main bottom steel.
If you have a load bearing internal wall in the basement then you have a two span beam. You still get tension in the bottom of the slab as you approach the middle of each of the two spans. However, you usually get tension in the top of the slab over the internal wall. Hence your main top steel.
It may be that the basement has been designed as a continuous box. In effect the concrete and reinforcement work together at the corners (often called a moment connection) as opposed to say the basement floor and walls acting together with the suspended slab only designed to prevent the basement wall heads moving inwards and to carry the loads from above this is more of what is called a pinned connection.
If this is the case then you also have tension in the top of the suspended slab and the outside of the vertical basement wall at and near this junction thus you need some steel in the top and outside of the vertical walls and this can be a congested area.
You can ask the Engineer how the design works, often they are more than happy to explain. It’s worthwhile to know how something stands up, especially when you are finished the project and enjoying the fruits of you labour in front of the fire on a windy winters night.