Hello.
I work with WordPress for 3 years now and know basically everything about it. I worked with really 'fat' websites recently, so I can help you with your too. And as you see, I don't ask for much money, because I don't think that's the kind of job you need to pay a lot for.
Anyway, full cleanup will take 1 day (about 10-12 hours), including everything you pointed to and even more. I know a great way to speed WordPress website, so it loads much faster and takes less space. You can check out Google PageInsights tool, I will be referring to it. By the way, what is your score? I bet I can increase it a lot ;)
Hope to hear from you,
Victor.
P.S. You will more than satisfied with my work :)