Can I use 2 Power Supplies in series like this?
The power supplies you have illustrated are actually connected in parallel. This setup should be totally fine, and is in fact the defacto method of connecting circuits to the mains.

Consider how you may have multiple 5 V supplies plugged into a power strip. Each of these supplies would be connected to the same 2 nodes, live and neutral, and are therefore in parallel. They then convert the mains supply into the required format, in this case 5V.

Edit: here is an equivalent circuit you could use to visualise the connections. The two power supplies are referenced from the same ground node and should cause no problem to each other.







simulate this circuit &ndash; Schematic created using CircuitLab