<think>
Okay, I need to implement the thaw_row function according to the problem description. Let me start by understanding the requirements.

First, the function takes a string representing a row of cells, where '#' is ice and '.' is meltwater. Then, a number of steps. Each step, ice cells that are at either end of the row or adjacent to meltwater will melt. But the melting happens simultaneously for all cells in each step. Also, the function needs to validate the inputs: the row must be a non-empty string, only contain '#' and '.', and steps must be a non-negative integer. If any of these checks fail, a ValueError is raised.

Looking at the current code, the function has a check for the row being a string and not empty, but the other validations are missing. Also, the steps need to be checked for being non-negative.

So, first, I need to add the validation checks. The row must be a string, not empty, and all characters must be either '#' or '.'.

Then, for the steps, if steps is negative, raise an error.

Once the inputs are validated, the next part is simulating the steps. Each step, we need to determine which ice cells will melt. But since the melting happens simultaneously, we need to mark all the cells that will melt in this step, then update them all at once.

How to approach this? For each step, create a list of indices that are to be melted. For each cell in the row, check if it's ice ('#'). Then, check if it's at either end (i.e., index 0 or len(row)-1), or if it has a neighbor that is meltwater ('.'). However, since the melting is done in parallel, we need to check the original state of the row for each cell, not the updated one.

So, for each step, we can create a list of positions to be melted. Then, in the next step, we can update those positions.

But how to do this efficiently? Let's think:

For each step, iterate through each cell in the row. For each cell, if it's ice, check if it's at the end or has a neighbor that is meltwater. If so, mark it for melting. Then, after processing all cells, update those marked positions to '.'.

But since the melting is done in parallel, we can't process the row in place during the same step. So, we need to create a list of booleans indicating which cells will be melted in this step, then apply those changes.

So, the steps would be:

1. Validate the inputs.
2. For each step from 1 to steps:
   a. Create a list of booleans indicating which cells will melt.
   b. For each cell in the row:
      i. If it's ice ('#'), check if it's at the end or has a neighbor that is '.'.
      ii. If yes, mark it for melting.
   c. Update the row by changing all marked cells to '.'.
3. Return the final row.

But how to check the neighbors? For a cell at position i, check left (i-1) and right (i+1) positions. However, since the melting is done in parallel, the original state of the row is used for checking.

So, for each cell in the original row, check if it's ice. Then, check if it's at the end (i=0 or i=len(row)-1), or if either left or right neighbor is '.' (in the original row).

Wait, but during the same step, the melting is done in parallel. So, the check for neighbors is based on the original state of the row before the step. So