What is the proper method of installing JCE? I have tried installing it into the master site but it does not show in the slaves. I am using separate dbs for each site. Thanks.

When a slave site already exists, once an extension is installed on the master, , you have to re-install the extension on the slave sites where you want to also use it.

Tried that, every time I try to install something I get the message

"Unable to find install package"

In the Joomla package installer.

This is a Joomla standard error message that may happen when Joomla is not able to upload of the package or when it is corrupted or thing like that.
If you are sure able to open the tar, you may try to deploy the tar into a temporary directory and try to install it from this temporary directory.
This will avoid the Joomla upload and probably will help you.
This kind of problem may also happen when the PHP configuration has a too small upload size defined in php.ini.

Ok, tried that. I am now getting:

"It was not possible to copy the selected file."

...since JCE is already installed on the host domain.

JInstaller::install: Failed to copy file:
/var/www/vhosts/mysite.com/httpdocs/multisites/slavesite.com/tmp/com_jce_150/com_jce_150/site/index.html
to
/var/www/vhosts/mysite.com/httpdocs/components/com_jce/index.html

I also changed the tmp and log paths to the /multisites/slavesite.com/tmp and /logs folders. Is this a normal step??

NO this is not a normal procedure.
I suggest you this procedure to help you identify the reason.
You say that JCE is already installed on the master website.

Until here, this is not what I see.
What I see is that it does not want to copy the temporary file to the target place.
The copy should work if you have correct permission.
I susspect that if you try to copy the file with the same "user" than the one used by Joomla, you will have the same problem.
I suspect that you have a different owner than the one corresponding to the httpdocs/components/.
You have to check the permission and perhaps fix the problem of owner that could be resulting of an installation of fresh Joomla with a FTP and a root user.
When a normal user will try to create file or folder, it will be rejected by insuffisant permission.

When you install a component from a directory, you don't have to change the log and the tmp.
This is again the symptom of a permission problem.

If you don't know how to fix the owner, you can try to give all permission by a chmod 777 on all the files and folders. (This is not recommended for the production, but will help you install the files and will help you to see the owner and group used for the installation).