There are a few issues with your updated layout:
In a wet-vent, the toilet needs to be the last fixture connected (or be connected via a symmetrical fitting). Your updated sketch has the shower connecting downstream of the toilet. To fix this, you would need to install a 3" double tee (you don't need the wye and 45° as you can change from horizontal to vertical with a 90° but vertical to horizontal with two 45°s). One side would connect to the toilet and the other side would be bushed down for the shower. This is sometimes called a 'potty on the post'.
The vertical distance on the shower may exceed what your code allows, this would be addressed in the above revision as the p-trap would be moved up.
As far as installing pipe within the footing, that will depend on your local authority. Here we can do it if required so long as the pipe is wrapped in sill gasket (~1/8 thick foam wrap) to allow for some separation between the pipe and concrete.
I would make a few changes:
Take a more direct route to the sink, eliminating some of the 45° fittings (this eliminates a lot of the tight turns and should be less likely to plug)
Combine the vertical sink and vent pipe into one 3" vertical pipe (creating a wet vent for all fixtures)
Eliminate the s-trap on the shower and use a p-trap
Here's a sketch of the above changes:
This would be to code in Canada but I'm not sure of where you live and any differences between codes. For the most part, codes in the USA are close to Canada with small differences and different terminology.
If this is the only plumbing in your house/building, there may be a code requirement that the vent stay 3" to roof as they typically call for one main vent of that size.