Am I stuck with my freelancer's decisions and work on my blog?

I had some dudes in India freelance me a media upload web-site, a while ago, on my Godaddy hosting. I'm going to take a split-second breather from my invulnerable chess engine to work on this again.
The product was fine, but I'm reluctant to ask for new updates, because they've fleeced me on updates before. They've probably removed the project from their dev.
It's complicated, but I was hesitant to suggest changes after my Freelancer uploading functionality had been completed. They were mainly aesthetic changes, and threatened to charge me more hundreds of dollars. ( The contract was for the media, and they did that)
It is a standard Wordpress looking template, ( EDUCON ) but
I am reluctant to make changes, in case it destroys what they've coded / done, and I'd prefer not to contact them again. I did a political blog once that broke the Adsense payment threshold. They didn't add the adsense code locations on the layout. They basically said, we've done the coding, now get lost. If I do the adsense stuff, will it destroy the media upload work they've done? If I look in the WP menu panel, is that all solid? - won't alter with aesthetic changes?
The template they chose was lame, and I went with it, so they could get functionality done. There's no room even for an intro paragraph or welcoming type stuff. I need that space for Adsense boards. I have an extended template selection product. more Themes   -  it says 9 themes
If I paste adsense code into a widget, will I be able to place it anywhere on their page? I doubt it, they made their own 'manage media' button, because the horizontal EDUCON menu couldn't fit another text-link. I suspect I can not change theme, because their 'manage media' button would get destroyed
Am I stuck with their work?

beavoidSelf EmployedAsked:
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Shaun VermaakTechnical SpecialistCommented:
Impossible to say without access to the actual site and original theme.
A line-by-line comparison can be done with a version control application and chances will have to be investigated, one-by-one

Is this the theme?

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beavoidSelf EmployedAuthor Commented:
Yes, but they only used the horizontal menu and a downwards blog roll
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