I think it's a hard question to answer as it could be so different depending on the project.

Ideally, your projects should be deployable independently from the other ones, to a certain extent. As an example, your API projects should get deployed, then the other ones using that API can be deployed later, be it a few minutes later or even days.

Hopefully I answer part of your question here?

For deployment, "it depends™" but you can certainly do whatever you need to do, always a matter of time and money! :) Your CI server could kick something on your servers. I encourage you to look at the hosted CIs and their documentation.