Easy-peasy. Most hosting services handle this. My current hosting did this for me so I never had to worry about it.
Assuming no links are broken, then that's fine. Otherwise 301 redirect broken link to homepage or relevant pages. Assuming your domain registrar remains the same, then it's fine. Otherwise set TTL as automatic or almost zero. Cloudflare handles this.
And of course your destination host should not be down. I use a VPS and that's never been an issue with migration. If you don't want to get your hands dirty, let your host tech support do all the hard work for you.