Can we run windowservice or EXE in Azure website o

I have experienced with cloud service/hosted service on Azure. However regarding another project i am confused in selection in terms of functionalities.

I have project (2 tier asp.net app) with that i need to run windowservice or exe which will do some functionality every day (like fetch data) so my confusions are as below

Regarding Windows Azure Web Sites

Can i access RDP if i'll move to reserved instance?
can i run windowservice/exe ?

Regarding Windows Azure Virtual Machine

Is it same as dedicated server?
can i use WASD as database from application reside in same? I think i can run any exe and installed anything however azure is going to recycle this and if yes then what happened on recycling?
can i use new window server 2012 (VHD) in that?

Azure website & VM both are in preview mode so is it reliable to use it as production version?

As far as Windows Azure Web Sites WAWS go: No, you can not RDP into the instance even if you are reserved that I know. Also, you can not run a windows service/exe on the WAWS. If these are requirements of yours then you want to run either a Virtual Machine or use some start up tasks on a Cloud Service.

With a Windows Azure Virtual Machine (WAVM) you may install a service, or pretty much anything you can install on your on premises servers. Note that licensing is up to you to figure out beyond the license for the OS (or for SQL if you are using the SQL image from Microsoft). Yes, you can use/reach Windows Azure SQL Database from the virtual machine, but it doesn't reside on the Virtual Machine, that is still a hosted service. You can install (or choose to use the premade image) for SQL Server on the VM; however, as you point out this can go down or get recycled. Currently they do not support replication; however, they do support mirroring to deal with the issue of the boxes being down from time to time.

They release Windows Server 2012 as an image (thus making it available) for Windows Azure VMs late last month I think.

As for using these systems for production use, they are in preview and thus I'd say that all the legalese will say you should not use it for production at all. Your mileage may vary and note that until it is out of preview there is no official support for these features beyond what you get from the forums and here on stack overflow; however, if you have something really compelling you should reach out to your local Microsoft rep to talk about your needs.