Learn Russian: Врач думает о здоровье.

The preposition о means "about" and is used before words starting with a consonant, like здоровье (health). You only change it to об when the next word starts with a vowel sound, just like how "a" changes to "an" in English.

Since о (about) usually makes the next word change its ending, why does здоровье look exactly like its dictionary form?

The preposition о requires the Prepositional case, which usually means replacing a noun's ending with an -е. Because the neuter noun здоровье already ends in -е in its dictionary form, its ending in the Prepositional case happens to look exactly the same!

The letter ч is a soft sound. Why isn't there a soft sign (ь) at the end of врач?

Even though ч is always pronounced softly in Russian, spelling rules depend on gender. Masculine nouns ending in sounds like ч, ш, or ж (like врач or муж) never get a soft sign at the end. Only feminine nouns like ночь (night) add the ь.

How is the verb думает (thinks) formed?