Currently we have a Rackspace cloud server (LAMP) with no setup for elastic search.
1. Does this extension needs an existing elastic server setup?
2. Do we get full support on initial setup and installation?
Thanks in advance.
What extension are you referring to?
Could you clarify your questions?
If you want to run Elasticsearch on your Magento store, it will first need to be installed at the server level.
Whether you receive full support for it or not will depend on Rackspace Cloud. You should contact their support to confirm this.
I've started to use the cloud service from Rackspace last december (the product is a PaaS so you can configure or change things inside your server)
They provide a ready to use instance to run Magento 1 (latest version at that moment).
If you want to use ElasticSearch you'll need to install the software on your server first and then the module into Magento.
About your second question, I guess that you can ask for that but I don't remember if it's included on the managed service or you'll need to pay extra.