Magento 1.9 Migration Issues After Moving Hosts

Good morning.
I'm still pretty new to Magento since I started using it not too long ago.
My company had to change webhosts because our previous host didn't have Cronjobs.
Now after moving all the files, a lot of sites won't open.
This is the site.
The backend also changed from url/admin to url/index.php/admin for some reason.

Can anyone please help me with this? Thanks in advance.

edit04:
When I first installed Magento onto the server, I had to clear all .htaccess files because they had something in them that was not compatible with our host. But since then it has been working fine. Whatever fine is in this case. At least the backend doesn't give me any trouble.

edit01:
That's how my .htaccess looks right now:

############################################
## enable rewrites

    Options +FollowSymLinks
    RewriteEngine on

############################################
## you can put here your magento root folder
## path relative to web root

    #RewriteBase /magento/

############################################

edit02:
If I add the .htaccess file into main directory, the site stops working.
(Unless it changes back to url/admin)
In the config/web the "use server rewrites" option is on

edit03:
So it does not just change back to url/admin.
This is what happens everytime I add the .htaccess file into "magento/"

Internal Server Error

The server encountered an internal error or misconfiguration and was unable to complete your request.

Please contact the server administrator, admin and inform them of the time the error occurred, and anything you might have done that may have caused the error.

More information about this error may be available in the server error log.

Additionally, a 404 Not Found error was encountered while trying to use an ErrorDocument to handle the request.