Hi there, I too am rather new to modding (still trying to figure out how the heck to get capital ships over level 10), but I should be able to answer most of these questions 
1.)I'm not sure exactly what you're referring to here, but I assume the Vasari's "Phase Gate"? If so, the quickest and easiest way to do this would be to open each races "Player_.entity" file, add 1 to the planetModuleInfo..Page:1..Count, and add "entityDefName "PLANETMODULE_PHASEORBITALPHASEGATE"... You'll also have to figure out what to do about the research prereq. Either remove it from all the PhaseGate.entity files , or add this research to the other races as well. If you want to remove the "summon fleet" ability for the other two races, just don't include the research for it 
2.)you can change many aspects regarding pirate raids from the "Gameplay.constants" file. Just search in the file for "pirateRaidDef" and "buildSpeedData-Slow". Everything between those two search results deals with pirate stuff... This of course would not be a "per-map-basis", but would affect all maps. You could increase the pirate threat on a per-map-basis I guess by adding more pirate bases
Other than those 2 methods though, I have no idea
3.)Yes. All three races have a "capital ship purchasable level" research that caps out at 2 or 3 (can't remember as I've changed all mine to 8). Just either change these to 8 like I did, or make the "per level bonus" a higher number to get to 10 by the lower cap. Also, take a look at the gameplay.constants file at what is typed after "upgradePriceForNextLevel" which shows up 10 times (one for each "ExperienceLevelData"). Make sure the numbers are set to what you want them to be. The file by default does have numbers set for each but they make no sense at the higher levels.
4.)2 ways (1 quick and easy, the other a not so much). The slow way is to edit every "PlanetModule_Whatever.entity" file and cut the "BuildTime" in half. A faster way is to change the "Gameplay.constants" file. Just change the "moduleBuildRateGameSpeedScalar" value (on the speed you usually play of course or all 3 if you want no variance) to 1.00 (that should be 2x as fast, but the answer might be .50 for .5x as slow...not sure which one is right, but the default for "slow" games is 0.00, and for "fast" games is .20)
5.)To change this just load up whichever race's PlayerWhichever.entity file, and look at the entries between "hyperspaceData" and "shieldData". Those are all the entries that affect hyperspace. Increase to go faster 
6.) By this I assume you mean just their normal travel speed (I believe they call this "subspace"?). If so, you can change this on a ship-by-ship basis by loading up all the different WhicheverRacesWhateverShip.entity files and changing the values for the following entries found in all those files:
maxAccelerationLinear 200.000000
maxAccelerationStrafe 10.000000
maxDecelerationLinear 500.000000
maxAccelerationAngular 3.300000
maxDecelerationAngular 9.999996
maxSpeedLinear 800.000000 This example was copied from FrigatePhaseLight.entity This means it is a FRIGATE belonging to the PHASE race (Vasari, PSI is advent, and TECH is Tec), and it is the LIGHT variety frigate.
7.)to increase those incomes, load up each races trade and refinery frigate .entity files, and increase the number after "maxCargoCapacity" (example: FrigatePhaseTradeShip.entity is the tradeship frigate spawned by the Phase races Trade ports.) The number of frigates spawned per port/refiner is determined by the port/refineries Planetmodule.entity file, and increasing this also boosts income...this method however also negatively affects performance as you'll have a lot more little ships flying around for the computer to think about 
8.)Just load up the fleet capacity research for whichever race you want to change for the stage you wish to achieve this at, and change the "Perlevelvalue" to be whatever you want that research level to add
Example: open "RESEARCHSUBJECT_MAXSHIPSLOTSPHASE0.entity", and make the below change
researchModifier
modifierType "ShipMaxSlots"
baseValue 100.000000
perLevelValue 100.000000 -----> 90000.000000
This will cause any Phase (vasari) player to increase their fleet capacity from 100 to 90100 by learning the very first fleet capacity research. All the rest will still increase fleet capacity by their respective (puny) amounts, so no further edity needed... I'm not sure about this, but I believe that if you make "baseValue" be 90K instead in this file, then you won't have to research at all for that much.
Hopefully this helps you out!