Calling async functions on parallel threads in c#

I have a three async function that I want to call from multiple threads in parallel at the same time. Till now I have tried the following approach -

int numOfThreads = 4; 
var taskList = List<Task>(); 
using(fs = new FileStream(inputFilePath, FileMode.OpenOrCreate,FileAccess.ReadWrite,FileShare.ReadWrite))
{
    for(int i=1; i<= numOfThreads ; i++) 
   {
      taskList.Add(Task.Run( async() => {
       byte[] buffer = new byte[length]; // length could be upto a few thousand
       await Function1Async(); // Reads from the file into a byte array
       long result = await Function2Aync(); // Does some async operation with that byte array data
       await Function3Async(result); // Writes the result into the file 
      }
   }
}
Task.WaitAll(taskList.toArray());  

However, not all of the tasks complete before the execution reaches an end. I have limited experience with threading in c#. What am I doing wrong in my code? Or should I take an alternative approach?

EDIT - So I made some changes to my approach. I got rid of the Function3Async for now -

for(int i=1;i<=numOfThreads; i++) 
{
   using(fs = new FileStream(----))
   {
      taskList.Add(Task.Run( async() => {
       byte[] buffer = new byte[length]; // length could be upto a few thousand
       await Function1Async(buffer); // Reads from the file into a byte array
       Stream data = new MemoryStream(buffer); 
       /** Write the Stream into a file and return 
        * the offset at which the write operation was done
        */
       long blockStartOffset = await Function2Aync(data); 

       Console.WriteLine($"Block written at - {blockStartOffset}");
      }
   }
}
Task.WaitAll(taskList.toArray());

Now all threads seem to proceed to completion but the Function2Async seems to randomly write some Japanese characters to the output file. I guess it is some threading issue perhaps? Here is the implementation of the Function2Async ->

public async Task<long> Function2Async(Stream data)
{
        long offset = getBlockOffset(); 
        using(var outputFs = new FileStream(fileName,
            FileMode.OpenOrCreate,
            FileAccess.ReadWrite,
            FileShare.ReadWrite))
        {
            outputFs.Seek(offset, SeekOrigin.Begin);
            await data.CopyToAsync(outputFs);     
        }
         return offset;
}