No everything is available vs TF HCL, it uses CDK from AWS CDK and tries to bridge things to TF have codegen. There’s a lot of weird corner cases and inconveniences. It even uses React under the hood.
Pulumi at least takes care of it better. Maybe not perfectly but better.
Yes, pulumi is just wrapping terraform[1]. So you need to understand both the quirks of that and the quirks of pulumi. And I'm lazy so I just want to deal with one quirk at the time.
It depends.
The AWS "Classic" provider uses the terraform provider [1].
The AWS "Native" provider does not, and instead uses the AWS Cloud Control API [2].
[1]: https://github.com/pulumi/pulumi-aws
[2]: https://github.com/pulumi/pulumi-aws-native