No. Also, the correct term would be "renewed", which, technically, is just a brand new certificate, but just with the same hostnames as a previous certificate.
Yup.
Above is all assuming there still exists a CAA record, but just without letsencrypt.org as a value (i.e.: one or more CAA record(s) with non-Let's Encrypt CAs as value).
If NO CAA record is present, there is nothing preventing issuance by Let's Encrypt (or any other CA for that matter).