Learn Arabic (Modern Standard): حبذا اللباقة!

No, حبذا is entirely fixed. It acts as an invariable expression of praise. Even though it is historically made of a verb and a demonstrative pronoun, they are fused into a frozen unit that never changes for gender or number, no matter what noun follows it.

What case ending should اللباقة take in this sentence?

It takes the nominative case, pronounced as اللباقةُ (al-labaqatu). The noun being praised after حبذا is grammatically treated as a delayed subject, so it must always take the nominative case.

Where does the ذا at the end of حبذا come from?

It is the demonstrative pronoun ذا (dha), meaning 'this'. The phrase حبذا literally translates to 'Loved is this...' or 'How excellent is this...' followed by the noun. However, in Modern Standard Arabic, the two parts are completely fused together and function as a single exclamatory word.

If I want to express the opposite and criticize tact, how do I negate this sentence?

You simply add لا (la) to the beginning, making it لا حبذا اللباقة (la habba-dha al-labaqatu). This forms the fixed expression for subjective blame or dislike, meaning 'How terrible is tact!'