The FleetSupplyData section in gameplay.constants is the multiplier that's applied to all fleet point gains when you have small/normal/large selected. So with the 1.25 setting on on Large, every time you get fleet points you get 25% more (125 instead of 100, etc).

So modifying this value is the quick and dirty way, if you set it to something like 2.0 you'll just get double the FP each time.

The other way is to modify the individual research techs to create whatever progression you want.. which I like better, but it's more work. If you want to go that way I can explain how those work. Otherwise just play around with gameplay.constants.

I can't speak for the SoA2 mod and how their settings are, though.

Okay, for the individual research techs, each race has their own lines for capitals and fleet points. For example,

RESEARCHSUBJECT_MAXCAPITALSHIPSTECH0 -> 7 (8 ranks of research for capital crews)
RESEARCHSUBJECT_MAXSHIPSLOTSTECH0 ->7 (8 ranks of fleet point research)

PSI/PHASE have their own.

It starts off with 0, where you have

researchModifier
 modifierType "ShipMaxSlots"
 baseValue 100.000000
 perLevelValue 150.000000
researchModifier
 modifierType "IncomePercLost"
 baseValue 0.000000
 perLevelValue 0.093750

The first subject is the only one that has a "baseValue" set, it's what you start the game with before you perform the research. In the default case on Normal, you start the game with 100. The perLevelValue is how many fleet points/capital crews are added to your current total when you perform the research. So researching the first rank will give you an additional 150 fleet points (modified by the multiplier in gameplay.constants if you're playing with Small/Large fleets) to a total of 250. The next researchsubject file (1) has no baseValue set anymore, and has another perLevelValue of 150, to bring you up to 400 total. So on so forth!

The files for capital ships function the same way, only they add capital crews instead of fleet points.

The next block is for the percentage of income upkeep that gets added on when you do the research, and by default each rank adds an additional 9.375% upkeep.

What do you mean by default race names? Like the empire names given to the AI players, or the names of the races themselves (TEC/Advent/Vasari)?

You'll have to download the forge tools pack (the downloads button at the top of the page) which contains the Reference Data with all the GameInfo files in text.

For the empire names, each race has their own as laid out in their respective .entity files. For example in PlayerTech.entity you have:

aiNameData
 nameCount 10
 name "IDSPlayerAINameTech0"
 name "IDSPlayerAINameTech1"
 name "IDSPlayerAINameTech2"
 name "IDSPlayerAINameTech3"
 name "IDSPlayerAINameTech4"
 name "IDSPlayerAINameTech5"
 name "IDSPlayerAINameTech6"
 name "IDSPlayerAINameTech7"
 name "IDSPlayerAINameTech8"
 name "IDSPlayerAINameTech9" 

Which correspond to tags in the English.str file. I don't have the string file here at work, but each string is set up with an ID, like IDSPlayerAINameTech0, and Value, which is the actual displayed text. So if you change whatever value that tag contains, next time the game randomly selects it, your new name will show.

Yes, basically. Just make a new folder for your mod in the mod path (ingame go to Options > Mods > show mod path), extract the text GameInfo into that folder (and the String folder with English.str if you're going to modify the names) and then make all the file changes there. Then just enable the mod in-game! You can also read the sins_modset.pdf in the Documentation folder in the forge tools archive for an overview of how to put together a mod.

Did you add the modified \String\English.str into your mod folder?