You can definitely set Gmail to go from conversation to conversation (or message to message, if you have conversation view off) as you delete messages rather than back to the inbox. This is under Settings, Advanced, Auto-Advance. Auto-Advance is disabled by default.
To my knowledge there is still no way to change the sort order as far as most recent being last and oldest being first.
Brian - Windows 10 Home, 64-Bit, Version 1803, Build 17134
A little kindness from person to person is better than a vast love for all humankind.
~ Richard Dehmel