For the purpose of this question, let us assume the contract is for common goods and services.
Lets say I meet a Plumber over some online marketplace (e.g. Facebook, Craigslist, etc) and he writes that he will fix so and so problem with my bathroom while guaranteeing that he will pay out-of-pocket for any potential unexpected damages that might be incurred during the repairs (e.g. flooding of my house if he proves to be incompetent).
Another hypothetical scenario is where I commission a local graphic designer to create a logo for my new business. During the negotiation phase, the graphic designer acknowledges that he will hand over all copyright claims to the newly created work once he has been paid. The designer makes this pledge via an email, as opposed to a signed written agreement.
In either scenario, are their promises legally binding?