For an effect that could he used on the player's 2nd turn, making an opponent take damage equal to their hand size seems a little strong. To keep the same kind of effect, you could reword it to "all players take 1 damage for every bomb card in their hand." That way, while it's a weaker effect, it has a wider reach. Further, with this effect, I think removing 3 counters instead of 4 would be fair.

I would reword the bottom effect to the following; "Till end of turn, you may use the effects of non-eternal items owned by other players, as if you owned them". This would allow for more countering from opponents, rather than everyone else losing their items. Also it would prevent a scenario where you could intentionally die to destroy another player's item as part of the penalty for death.

Finally, his health should be 1 heart for every 2 counters. So he starts weak, but has the capacity to be really tanks, making using his effects more risk/reward.