Booming blade, average 22 damage.
Only if he moves, which he does not have to do.
The Hound is attacking with advantage (Pack tatics) him for extra 10 damage and chance prone.
The Hound has 2 attacks with advantage per turn (normal attack and oportunity attack), both with prone chance and critical chance. 44 average damage per turn if all hits (All attack has advantage)
They are not all at advantage.
To start with the hound can't see in darkness and because of that can not possibly get advantage. The sorcerer also loses his advantage if casting any ranged spells if the hound knocks the enemy prone.
Prone imposes disadvantage unless you are within 5 feet and using a ranged attack within 5 feet also imposes disadvantage. This means if the hound knocks the bad guy prone you (the sorcerer) no longer advantage on anything except melee or touch attacks.
As a matter of fact the adversary can take away your advantage on scorching ray "shenanigan" simply by crawling the last 10 feet up to you and attacking you from the prone position. That would make him "prone" when the OA occurs and since he is 10 feet away you would have prone disadvantage to cancel the unssen attacker advantage. Further since your reach is 10 feet, you can't do booming blade as a reaction since it occurs at 10 feat away. So in reality all of your "warcaster shenannigans" are not at advantage, they are a straight up roll.
The Shadow Sorcerer can summon another The Hound on next turn
You can't summon another hound because you don't have enough sorcery points (you empowered your booming blade remember). 2 for darkness plus 3 for the first hound plus 1 for empowering booming blade is 6 and you only have 8.
A STR 20 fighter with PAM level 8, deals around 29 damage per turn without aditional effect. (without advantage).
No you are wrong. An Eldritch Knight fighter with 20 strength and great weapon fighting style and a +2 weapon who is going NOVA like you are is going to hit for
67 That is:
Booming Blade: 1d10+1d8+7 (rerolling 1s and 2s)
Warmagic: 1d10+7 (rerolling 1s and 2s)
Action surge booming blade: 1d10+1d8+7 (rerolling 1s and 2s)
plus 4d8 when the enemy moves.
That is without any "warcaster shenanigans" ..... which of course he could also do as well.
The difference is the EK can do this again after every short rest, while you can't summon another hound for the rest of the day and he always rerolls his 1s and 2s and does not need to use empowered spell to do it.
In addition to this he can heal himself, gets hit less, has more hps and has higher attack rolls.
This is also not by far the most powerful fighter build possible.
16 AC with disadvantage and immunity to oportunity attack (Darkness) is much better than 19 AC fighter. Bealive me. If put Shield Spell inside math, it's unfair.
No it isn't there is math in play here.
Inside darkness with a 16AC the chance of hitting you is 36%. The chance of hitting a 19AC Eldritch Knight (and it should be 20 by the way) with shield spell is 20% and that is if he attacked the first turn instead of casting a defensive spell like you did. If he cast blur on himself to start the combat then you are NINE TIMES more likely to be hit.
It is not unfair to put the shield spell in play, you are just choosing a different (and less effective) reaction. Even if we play by the same rules though and the EK has the same PAM and warcaster feats and he does the same OA trick you are using after casting a defensive spell (blur) on his first turn, he is still only hit 20.25% to your 36%. That is without the shield spell ..... and he has more hit points to boot.