Going through this logically:
Who we are currently hosted by?
There are several sites that will show you who is hosting a particular site. Here's one, enter your site address into the search box.
Once you've established that, you probably need to talk to whoever pays the bill. Your finance dept? Then liaise with the hosts armed with your company's details.
Who our current Site Admin is and how to change it to myself?
You need to ask the hosts about login information for the hosting account. Once you're in there, you need to obtain FTP details so that you can FTP to the site or maybe gain access to the phpmyadmin interface.
With either pieces of info, read this page and take one of the suggested actions:
Once you've reset the admin account/password you can log in and assess the site.
Any suggestions on slow load times?
Only after you've addressed the first two points and posted the link to your site in here.