It appears you're talking about this leaderboard.
You'll have to contact that leaderboard's moderators (you can join the Discord server on the left) and tell them to fix this. They'll have to select the "Timer asc." option in the category, but since they're using a subcategory, they may have to create a new Full-game category with all Longest Game runs.
@Zvezdi0708 The original post is talking about game requests, not submitting runs.
@Lieutenant_Boo They're talking about how splits.io displays on the site below a run--the times displayed are the RTA times regardless of whether it or IGT is selected as the default time on the splits.io run. It's not the only issue with how splits.io is handled on this site, but it doesn't seem like the site mods are treating it as a priority. I suppose posting a reminder on the site bugs thread wouldn't hurt.
Read Minecraft's "Game Rules", accessed by clicking "View Rules", then "Game Rules". There, it says that you must select "F3" if you use it during a run, so it's allowed.
Which is a tiny bit disappointing, since surely speedrunning based on real-world environments would be a fun experiment... Regardless, if you're committed, there's nothing stopping you from setting up your own leaderboards elsewhere.
You'll have to request the games you want on the site's thread. Make sure to read the rules fully and don't set your expectations high--the way you describe the game here, there's a good chance it'll be rejected. Unless you want to purchase a 3DS capture card or use homebrew, I'd just point a camera at the screen.
This is already possible on the site (see this leaderboard I moderate for an example). Make sure that your game's moderators have created "Individual level categories".
The most popular timer program is LiveSplit. There's no timer programs for console: to add a timer live, you need a capture card to get the video from your console to your PC and a program like OBS Studio to overlay the timer over the video. Otherwise you could record your video and edit a timer in afterwards.