Are there any dependencies between Spark and Hadoop?
If not, are there any features I'll miss when I run Spark without Hadoop?
Spark can run without Hadoop but some of its functionality relies on Hadoop's code (e.g. handling of Parquet files). We're running Spark on Mesos and S3 which was a little tricky to set up but works really well once done (you can read a summary of what needed to properly set it here).
(Edit) Note: since version 2.3.0 Spark also added native support for Kubernetes