I believe I have exactly the same, first buck converter based on LM2596 and used it only to charge lead gel 12V battery from 24V, 1A solar panel (~20W rated). No problems so far, though not a recommendation for either, they are all quite cheap and not isolated.
Arduino Nano: minimum perhaps 20mA (when idle).
1602 LCD: for circuit ~1.1mA + back light can draw even 130mA (actually can be controlled and be much less, if only dimmed lights are enough). Depending on model.