Incorrect. Fake Patch is only the updates to fallout3.esm. The 1.5 vs mods problem is in the exe.
Oh, awesome news! Very good to know, thank you.

So it seems that my problem lies elsewhere. I honestly don't know what to do, never had any problems with this mod.
When I disable it, I get the exp for kills in real-time without any problems. Whit it enabled I get the exp only from kills done in Vats-mode, and 1 in 10 in real time.
I tried changing load order and nothing helped, I have tried waiting for 4 days in place where there was no NPC (I'm using the MMM) and still nothing.
I hope someone might help me, in any case here is my load order:
Fallout3.esmFakePatch_v1.5.0.22.ESMAnchorage.esmThePitt.esmCALIBR.esmFOOK.esmMart's Mutant Mod.esmUnofficial Fallout 3 Patch.espUnofficial Fallout 3 Patch - Operation Anchorage.espUnofficial Fallout 3 Patch - The Pitt.espSlower Levelling - very slow.espDarNifiedUIF3.espDUIF3Extras.espAmplifiedCrippledEffectsV1-3.espGalaxyNewsRadio100[M].espRealFragGrenade.espAuto Aim Fix v1.1.espVATSFixOff.espUPP - Original Perks.espUPP - Pack 1.espFellout-SOTD.espFellout-Anchorage.espEnhanced Weather - Rain.espdD-Less Blood Time.espFOOK.espFOOK - Anchorage.espFOOK - The Pitt.espMyFOOK - NV Toggle - FOOK+OA.espFOOK - Anchorage hotfix.espFOOK - Tougher Enemies.espFOOK - Strength Requirements for Miniguns, Gatlings, 20mm Flak.espFOOK - Additional Power Armor Training.espFOOK - Reduced Armor Boni.espFOOK - Free Play After MQ.espFOOK - Owned!.espMart's Mutant Mod.espMart's Mutant Mod - Increased Spawns.espMart's Mutant Mod - Hunting & Looting.espMart's Mutant Mod - Tougher Traders.espMart's Mutant Mod - Zones Respawn.espMart's Mutant Mod - Natural Selection.espMart's Mutant Mod - FOOK.espTotal active plugins: 42Total plugins: 42
If anyone knows that something might be wrong, please do tell. I'll try to search for some sort of fix.
EDIT: So, I have deleted the old mod (but my experiance gained was the same even though it shouldn't be like that) and I have installed choose_XP (http://www.fallout3nexus.com/downloads/file.php?id=2812) - so far I have been getting exp with no problems.
Default values, low, high etc. all give me experiance points. Maybe the slower leveling mod was incompatible with the fake 1.5 patch, maybe with some other mod, maybe something just got corrupted. I don't know. After all it hasn't been updated in quite a while.
Cheers.