Welcome to the forum Neofit!
Before i go to AI diffculty improvements i'll say that there is no mroe challenge than to play real people. For this go to
http://seiv.pbw.cc
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SE4 never was easy. It does not matter that i complete every other strategy game with no difficulty, this one is realy though sometimes and i like that.
More difficult settings? Lets see.
-To make the AI more difficult, there is an option called "Computer Player Bonus". Low will not make much of a difference but Medium does change the odds. Never try High, from what i hear the AI will crush you early with its shielded, armored and heavily armed light cruisers while you're only building your early frigates.
-Put AI difficulty to High.
-Play with high number of AI enemies.
-Remove Neutral Empires by unchecking the "Generate random computer controlled Neutral Empires"
-Most important, download more races. There is the
http://universalshipyards.tripod.com but its going through a big overhaul and not too much of the races are Online (what you see there is barely a quarter from what i hear from John).
For the races part, i reccommend you to download the TDM-ModPack. Its a MOD which will enchance the AI difficulty greatly - many good modders put a lot of time to design a challenging AI.
Ask people here. I dont know much of which AI is challenging (my Taera isnt

) and i cant link you to the TDM because i dont know where to get it, but i am sure that someone else will do it.
For the ships setup.
You obviosly play with no AI bonus.
ECM is a must have with an intilligent AI because good players use both direct-fire and seeker weapons. Just to say if you employ ECM II against a race that does not have sensors, ohwell, you realy wont need armor or shields.
Sensors are the logical counter to the ECM (its the opposite if realy) and they allow you to still hit the ships that emply ECM.
Shields and Armors are both great things.
While i personaly prefer armor (the organic one

) the shields are a great tool when used together with everything else.
It does not matter how good do you play, if the AI is a decent one soon enough your missiles tactics will be countered by greater PDCs and shields and engines. And then you'll get hit.
Personaly to say, i find races that go strongly on seeker weapons an easy prey. Those ships are usualy hardly shielded and armored, and all you need is a single bLast from Ionic Dispersion Cannon to kill them (this cannon will destroy several engines leaving the ship unable to run at full speed).
Now once again, my personal tactics are to use varied direct-fire weapons as main and seeker artillery behind the front lines.
Overall, shield just does not allow damage to damage your ship but stops it at cost of its own energy. Another good thing is that shielded ships can never be captured unless shields run down.
Once shield's energy is depleted is stops functioning. If th ship survives the battle the shields will return in next battle. Overall, once shields are down the ship is ready to be damaged.
Thats when armor comes in play.
Armor is always damaged first. WHen shields are down, all the damage goes to armor. Only once all the armor is gone the ship itself can be damaged.
Now for the questions:
1.Yes this is still in effect. You gain no real experience by pointing the ship computer to the ship and pressing the big red button "fire". Unlike when you maneuver around the enemy peppering it with fire.
2. Ship experience is added to the chance-to-hit and decreases the chance-to-be-hit. Fleet experience should be added, AFAIK.
And no, ships do not carry the fleet expirience. If you disband a fleet you lost all the bonuses.
3. Dunno
4. I know of two ways to speed the population growth. First on the race setup there is a small nice option "reproduction". Add 10 and you will see an effect. Add 20 and your race will GROW _FAST_
Second the Organic tech tree has two facilites that will enchance the reproduction speed as well as a facility that will add a _fixed_ number of population to each planet in the sector. (but it is a lot to research the Last one)
5. Never had tried doing that. I do not even know does the AI accept of propose subjugations/protectorates. Maybe others here do?