Yeah in-game time is preferred, only Physical training needs you to calculate the true in-game time, other levels should either be in-game time if shown at the end or real time.

Hi yes you can do that exactly, on any level leaderboard page you have a "Submit run" button. The button should bring you to this page https://www.speedrun.com/nes_remix_2/run/new?level=Remix_I#Stage_1 where you can fill the game, stage, time and link to your video.