Learn Russian: Дети растут на похвале.

Not without changing the meaning completely. Ради похвалы (with the Genitive case) means "for the sake of praise" or "in order to get praise." This sentence uses на + Prepositional to show that praise is the "food" or foundation they grow on, much like the English concepts of "thriving on" or being "raised on" something.

Why do we use на + Prepositional (на похвале) to express what they "grow on"?

In Russian, на + Prepositional is often used to indicate what sustains someone or what they metaphorically "consume" to survive. You will see this same grammatical structure in phrases like жить на хлебе и воде (to live on bread and water), жить на одну зарплату (to live on a single salary), or сидеть на диете (to be on a diet).

As a quick refresher, what makes the verb расти (to grow) tricky to conjugate?

In the present tense, it is perfectly regular using the stem раст-: я расту, ты растёшь, они растут. The part learners often forget at this level is its past tense, which drops the -т- and shifts vowels: он рос, она росла, они росли.

Can похвала be pluralized here, similar to "praises" in older English?

Usually, no. In Russian, похвала is an abstract noun and is almost always used in the singular when referring to the general concept of praise, approval, or commendation.