Okay to start off with just do Points = Fan.
1 Fan = 1 point is simple to remain additive. The Faan Laak table, you can do that in the future. The Faan Laak table is like this:
http://mahjong.wikidot.com/rules:hong-kong-old-style-scoring
Scroll down to see the table. You earn fan and get into new sections that double the score. Similar to Mangan table from riichi. You can skip that for now though as straight 1:1 ratio and do additive is good enough.
The payoff rule I prefer is Discarder Pays 1x and the other 2 pay 50% rounded down. So if the discarder gives a tile for 7 fan the discarder pays 7 points and the rest pay 3 because 7/2 = 3.5 rounded down is 3.
Last tile on the live wall is under the sea which should be in the riichi rules already. If that's not what you're talking about then it's the last tile remaining of it's kind. Yes that one is strange and can be skipped. Not sure what double last tile it.
Self Drawing on a single chance 5 is the pattern I told you above the 4-5-6 just don't include it. But yes the description is implying that self draw and single chance are both implied in the hand you wouldn't add it together.
Double Last Tile don't include this either. It's trying to say you have two last chances on a double sided wait since there are only 1 of each of both your waits. This one is weird and doesn't need to exist.
I don't understand what going out and replacement tile is above. Going out just means winning aka mahjong. It's not a hand, maybe it means give points for winning which I would say don't include.
Replacement tile is like riichi, win after kong. Replacing the kong or replacing flowers. Winning on a kong replacement should exist, the winning on a flower replacement doesn't need to since no flowers.
Thanks Oliver, I'll help with all scoring questions as they come.