Well, there are really a few questions in one
A social media profile is like any web page: Having keywords there helps... It makes sense to craft a good short description (that mentions what you do and thus may include the keyword)...
Does using keywords within a Social Media profile (especially Facebook and LinkedIn) help improve rankings in the Serps?
A better question is, why would you care much? A social media profile is impossible to rank for a competitive keyword and even if you manage, it's lost battle because it's a poor landing page for that traffic anyway...
The only keyword worth ranking for, when it comes to social media profiles, is your brand name (to own another spot for your brand navigational searches)... which brings us to your next question:
Please see above; I'd recommend using your brand name there
Would you advise using a keyword in the Facebook URL or just the business name? Thanks in advance.
Everything will be ok in the end
If it's not ok, it's not the end