Write a Python function `sum_even_and_even_index` that takes a list of integers as input and returns the sum of all even numbers that are located at even indices in the list. Indices are considered zero-based, so the first element is at index 0, the second at index 1, and so on.
#### Example Usage
```python [main.nopy]
print(sum_even_and_even_index([5, 6, 12, 1, 18, 8])) # Output: 30
print(sum_even_and_even_index([3, 20, 17, 9, 2, 10, 18, 13, 6, 18])) # Output: 26
print(sum_even_and_even_index([5, 6, 12, 1])) # Output: 12
```
#### Constraints
- The input list will contain integers only.
- The list can be empty, in which case the function should return 0.