Basic Tajweed rules can be covered in 3 to 6 months with consistent classes. Reaching fluent application in recitation typically takes 1 to 2 years of regular practice.
No. You only need basic Quran reading ability. Tajweed is about pronunciation rules for Quranic Arabic, not conversational Arabic.
You should be able to read Arabic letters. If you cannot yet, start with our Quran Recitation course first.