Old Domain, New WordPress

I’ve been asked to develop a new WordPress site that will live on an existing domain and need help with making it happen.

Back story is that the current WordPress and FTP have login issues due to a past developer and my client now wants to start over from scratch basically. The plan is to open a new hosting account through DreamHost as well as a new WordPress account but still have the final domain name be ourwebsite.com, which the current wordpress site is running on. Just redirecting ourwebsite.COM to a domain like ourwebsite.ORG, .co, .net is not ideal as we would like the domain that is displayed while viewing the site to remain a .com.

Could we cancel the domain name and then repurchase it with the new hosting account?
It doesn’t sound like cloaking would work, I don’t want an extra frame.
Is it possible to transfer the domain from one hosting account to another? Both hosting accounts are on DreamHost.
What about the subdomains that redirect to ourwebsite.com? I have 6 to work with.