Develop. NET in sharepoint online

Hello, 
I'm Developer Sharepoint 2010 and am migrating to 2013 .. 
And I have some doubts about development. NET + SharePoint 2013! 

- I wonder if with the online sharepoint I can develop web parts and application page with Visual Studio and deploy to? 
- Apply the "Install-SPSolution" command in power shell? 
- Upload wsp in site settings-> Solutions ?
- How do I develop. NET in Sharepoint Online? 


Can anyone help me?

Thank you!