(i) To find the number of even 7-digit numbers, we need to consider the possible even digits that can be at the end of the number: 2, 4, 6, and 8.

For numbers ending in 2, 6, or 8, the remaining 6 digits can be arranged in \(\frac{6!}{2!} = 360\) ways (since there are two '4's).

For numbers ending in 4, the remaining 6 digits can be arranged in \(6! = 720\) ways.

Total even numbers = \(3 \times 360 + 720 = 1800\).

(ii) To form numbers between 20,000 and 30,000, the first digit must be 2. The remaining 4 digits can be chosen from 1, 4, 6, 7, 8.

The number of ways to choose and arrange these 4 digits is \(5 \times 4 \times 3 \times 2 = 120\).