Meşe ağacı yavaş büyüyor.

That -ı is the 3rd person singular possessive suffix, not an accusative case. In compounds where one noun “owns” or “of” another (oak’s tree = oak tree), Turkish often marks the head noun with a possessive suffix. So:

• meşe (oak)
• ağaç + -ı (tree + its) → ağacı
  Result: meşe ağacı “oak tree.”

This suffix also follows vowel harmony: stems with a back vowel like ağaç take -ı; if the last vowel were front (e/ü/ö/i), you’d see -i/-ü/-ö accordingly.

They look identical on the surface (both can appear as –ı/–i/–u/–ü), but here it’s possessive, not accusative. Two clues:
• Word role: meşe ağacı is the subject, not a direct object.
• Noun–noun compounds: possessive suffixes routinely appear on the second noun in such constructions.

If it were accusative, you’d be “marking” meşe ağacını as a direct object of a verb, but our verb büyüyor needs a subject.

When you talk about a whole class or species in Turkish, you often leave the noun in the singular:
• Meşe ağacı yavaş büyüyor. – “(An) oak tree grows slowly” (generally)
If you want to explicitly pluralize, you can say:
• Meşe ağaçları yavaş büyüyor. – “Oak trees grow slowly.”

Both are correct; singular feels more like a general rule, plural feels more like listing many trees.

1) Position: Turkish is typically Subject-Adverb-Verb (S-Adv-V). Adverbs normally come right before the verb they modify.
2) Form: Many Turkish adjectives double as adverbs without change. Yavaş can mean “slow” (adj.) or “slowly” (adv.).

• You can use yavaşça for a more nuanced or formal “slowly,” but in everyday speech yavaş is perfectly natural.

Both forms can express general truths, but with nuances:
• büyür (aorist) = “grows,” general habit or rule.
• büyüyor (progressive) = “is growing,” focuses on the ongoing process.

In many descriptive sentences about plants, animals or natural processes, the progressive is very common to stress that the action is happening or continues to happen.