GoDaddy really lived up to its bad reputation and recently changed their API rules. The rules are simple: either you own 10 (or 50) domains, you pay $20/month, or you don’t get the API. I personally didn’t get any communication, and this broke my DDNS setup. I am clearly not the only one judging from what I found online. A company this big gating an API behind such a steep price… So I will repeat what many people said before me (being right): don’t. use. GoDaddy.
Transfering a domain from one registrar (IE reseller) to another can be a pain, but yes you can - it normally involves a fee and manual actions from the registrars.
As long as the new registrar supports the TLD. A few Geo-TLDs can only be resold/managed by some registrars.
The easiest thing to do is to point the domain at ClouDNS nameservers.
Make sure you are happy with ClouDNS (I’ve never had issues with them) etc before committing