```python
"""Melt a row of ice one simultaneous step at a time."""
from typing import *
from collections import *

def thaw_row(row: str, steps: int) -> str:
    if not isinstance(row, str) or not row:
        raise ValueError("thaw_row expects a non-empty string row")
    
    if not all(c in "#." for c in row):
        raise ValueError("row must contain only '#' and '.' characters")
    
    if not isinstance(steps, int) or steps < 0:
        raise ValueError("steps must be a non-negative integer")
    
    if steps == 0:
        return row
    
    # Convert the row to a list for easier manipulation
    row_list = list(row)
    
    # Perform the thawing process for each step
    for _ in range(steps):
        new_row_list = []
        for i, cell in enumerate(row_list):
            if cell == "#":
                # Check if the cell is at the edge or has meltwater adjacent
                if i == 0 or i == len(row_list) - 1 or row_list[i + 1] == "." or row_list[i - 1] == ".":
                    new_row_list.append(".")
                else:
                    new_row_list.append("#")
            else:
                new_row_list.append(cell)
        row_list = new_row_list
    
    return ''.join(row_list)
```