first, my partner use "black garden", in my turn i summoned "inzektor earwig" (normal atk 1000) and end with 500, then i used "inzektor giga-mantis" eff to make him 2400 normal atk but didnt work.
second, the opponent summon a "light and darkness dragon" after that a chain of 4 was activated:
"eclipse wivern">"black garden">"light and darkness dragon">"variable form"
after that the dragon get his attack halved and none of the cards named before was negated...
later my partner used a magic card and the effect was negated by the dragon, in the next turn the other opponent (prophecy deck) used the field spell card "the grand spell booktower" and the effect wasnt negated... then he used "the high priest of prophecy" the effect activated in hand wasnt negated, and was summoned, after that he used his effect in the field and wasnt negated (again ._.), the dragon got 400 atk in that moment... so in my turn i think this: maybe he dont negate because he have 400 atk so im going to use effects. so i used foolish burial to have hornet in the graveyard but the effect was negated ._.

i dont understand what happen there, its a ruling error, bug or what?

That's quite confusing but ALL OF THEM are rulings error

first, my partner use "black garden", in my turn i summoned "inzektor earwig" (normal atk 1000) and end with 500, then i used "inzektor giga-mantis" eff to make him 2400 normal atk but didnt work.

From the wikia :

Enraged Muka Muka: If "Enraged Muka Muka" or "Red-Eyes Darkness Dragon" has its ATK halved by the effect of "Black Garden", then afterwards the monster's ATK does not change, even if the number of cards in your hand or the contents of the Graveyard change.

In that case, Giga-mantis change the original ATK of the monster. If it only affected the ATK, it would work anyway.

second, the opponent summon a "light and darkness dragon" after that a chain of 4 was activated:
"eclipse wivern">"black garden">"light and darkness dragon">"variable form"
after that the dragon get his attack halved and none of the cards named before was negated...

Here is LaDD's effect: When a Spell or Trap Card is activated, or the effect of an Effect Monster is activated, that activation is negated and this card loses 500 ATK and DEF
It negates the activation of a S/T not the activation of the effect of an S/T. It means it doesn't work on effects from continous spell or trap cards like Black Garden who is a field spell card. Also, like Stardust Dragon, LaDD must be chained to the negated effect.
If a SEGOC occurs and he's chained to the field spell, LaDD's effect will resolve but he won't negate anything due to his effect. He'll still lose 500 ATK/DEF when it will resolve.
Actual ATK of LaDD: 900 ATK

later my partner used a magic card and the effect was negated by the dragon, in the next turn the other opponent (prophecy deck) used the field spell card "the grand spell booktower" and the effect wasnt negated... then he used "the high priest of prophecy" the effect activated in hand wasnt negated, and was summoned, after that he used his effect in the field and wasnt negated (again ._.), the dragon got 400 atk in that moment...

Considering he negated the spell card, LaDD's attack became 400. If he got less than 500ATK/DEF, LaDD's effect cannot be activated. That's why he couldn't activate with all the other cards.

so in my turn i think this: maybe he dont negate because he have 400 atk so im going to use effects. so i used foolish burial to have hornet in the graveyard but the effect was negated ._.

i dont understand what happen there, its a ruling error, bug or what?

Now, the only explanation would be that he managed to gain some ATK which allow him to use his effect. If he still had 400 ATK at this point, it would be impossible for LaDD to activate its effect.
If the effect was negated nevertheless, it was probably because of another card, not LaDD.

Here is LaDD's effect: When a Spell or Trap Card is activated, or the effect of an Effect Monster is activated, that activation is negated and this card loses 500 ATK and DEF
It negates the activation of a S/T not the activation of the effect of an S/T. It means it doesn't work on effects from continous spell or trap cards like Black Garden who is a field spell card. Also, like Stardust Dragon, LaDD must be chained to the negated effect.
If a SEGOC occurs and he's chained to the field spell, LaDD's effect will resolve but he won't negate anything due to his effect. He'll still lose 500 ATK/DEF when it will resolve.
Actual ATK of LaDD: 900 ATK

about this, after the field spell card "the grand spell booktower" i try to use the plasma zone field for dark monsters but my card was negated like "foolish burial"... and like i said before "the grand spell booktower" wasnt negated when the opponent used it...

later my partner used a magic card and the effect was negated by the dragon, in the next turn the other opponent (prophecy deck) used the field spell card "the grand spell booktower" and the effect wasnt negated...

LaDD had 400 ATK after it negated the magic card. LaDD couldn't negate any effect anymore.

later my partner used a magic card and the effect was negated by the dragon, in the next turn the other opponent (prophecy deck) used the field spell card "the grand spell booktower" and the effect wasnt negated...

LaDD had 400 ATK after it negated the magic card. LaDD couldn't negate any effect anymore.

but he do it >.< he was with 400atk 2 turns, opponent and later my turn and he negated 2 of my cards

I'll try to test it tonight with a few friends. If you can duel before that, try to get a replay please.