To enter the dev menu of the RSDK-based games, set the DevMenu flag in settings.ini to true of the RSDK decompilations and press ESC at anytime during gameplay. If you're on mobile phone and/or inconvenient to press ESC, you can enter it in either the pause menu or options page in the game.
Set byte 0xCCB to 1 in the original SCD 2011's save file will also grant you access to the dev menu. The original Sonic Mania's method is the same as the decompilations. I haven't found a way to enter it in the original S1/2 2013 and Sonic Origins yet.
If you prefer the traditional level select like the ones in the Genesis original (or you just want to enter debug mode), tap S-E-G-A in order when started in a No Save game (NOT the Sega logo in the intro, but the one shown when you started a new save file) and hold two fingers on screen when you hear a ring chime. Alternatively, depending on the game, you could enter Sonic 1/Knuckles in Sonic 2/Sonic 3 codes on the title screens of the respective games. KiS2 code works outside Knuckles' gameplay, btw.
In case you're wondering, tapping A-G-E-S in order will swap Tails' name with Miles. It will also display the hidden credits in Sonic 1 when done in it.
Level Select is activated by default in the Simon Wai prototype, but you have to manually enter the Debug Mode cheat (C*4, U,D*4,U,A+Start). Once done, select a level, and hold A+Start until the level was loaded. After that, you can fully navigate the whole map by pressing B and move around the screen.
To be continued...