ERROR: S3 error: 400 (InvalidRequest): The authorization mechanism you have provided is not supported. Please use AWS4-HMAC-SHA256.

Solution :
Your s3cmd has older version, you need to upgrade it. Download latest one and use the file everywhere.
https://sourceforge.net/projects/s3tools/files/s3cmd/1.6.1/
I faced this problem on 1.1 version of s3cmd, I downloaded latest and got 1.6. After that I did not get the error.

How to use the downloaded folder.
1) Extract the folder and open it.
2) Now run your s3cmd command using this downloaded folder.

 /home/ubuntu/s3cmd-1.6.1/s3cmd ls s3://

/home/ubuntu/s3cmd-1.6.1/s3cmd -c /home/ubuntu/.s3cfg put /tmp/file.sql s3://bucketname

Server reached MaxRequestWorkers setting, consider raising the MaxRequestWorkers setting

There are three modules related to this settings. 
prefork, worker and event

First find which module is activated using

a2query -M

Now change its conf file in mods-available. 
In following case, prefork is enabled, so make changes in mpm_prefork.conf

Open file mpm_prefork.conf and increase the MaxRequestWorkers settings according to your RAM.

MaxRequestWorkers
A simple calculation for MaxRequestWorkers would be: 
(Total Memory – Critical Services Memory) / Size Per Apache process

In this case the server has 3400Mb of memory allocated, 
250Mb used by mySQL and each Apache thread averages about 30Mb. 
MaxRequestWorkers = (3400– 250) / 30
therefore MaxRequestWorkers = 105

Restart Apache. Check here too.

Cannot allocate memory: fork: Unable to fork new process in ubuntu

There are three modules related to this settings. 
prefork, worker and event

First find which module is activated using

a2query -M

Now change its conf file in mods-available. 
In following case, prefork is enabled, so make changes in mpm_prefork.conf

MaxConnectionsPerChild
If MaxConnectionsPerChild is 0, then the process will never expire.
Setting MaxConnectionsPerChild to a non-zero value limits the amount of memory that process can consume by (accidental) memory leakage.

MaxRequestWorkers
A simple calculation for MaxRequestWorkers would be: 
(Total Memory – Critical Services Memory) / Size Per Apache process

In this case the server has 3400Mb of memory allocated, 
250Mb used by mySQL and each Apache thread averages about 30Mb. 
MaxRequestWorkers = (3400– 250) / 30
therefore MaxRequestWorkers = 105

/etc/apache2/mods-available/mpm_prefork.conf

 <ifmodule mpm_prefork_module>   
    StartServers          5
    MinSpareServers          5
    MaxSpareServers         10
    MaxRequestWorkers       100
    MaxConnectionsPerChild  1000
</ifmodule>

Restart Apache.