Can I file a counter personal injury suit against my landlord to be heard at the same unlawful detainer hearing?

Probably not. Unless the personal injury claim is very closely related to the reason for the unlawful detainer, the suits involve entirely different matters and a judge would assume you are filing merely to delay the unlawful detainer action, which is supposed to be heard quickly. The personal injury claim would require several months before it would be ready to be heard, during which time you likely would not be paying any rent. The judge has the power to bifurcate [separate] the two issues and set one for trial and delay the other. Do you really have a valid claim or is this just to delay being evicted? Even if you won on the personal injury claim, that would have nothing to do with whether you should be evicted or not.

No, the UD court has jurisdiction only over the question of eviction. Be aware you will have to pay the jury for its time and may have to pay the other sides attorney fees if you lose.