I only started to work with the SharePoint, so I dont have so much experience. For some tests I need to install a SharePoint 2013 Server, we are using a SharePoint 2010 Server already in our domain as productiv server. Now I would like to install this 2013 Server in the same domain, that I can test with the usual domain accounts. Is this possible? Or should I better build a closed test environment?
There are some differences between SP2010 and SP2013. You can join the new server to the farm that is already created using configuration wizard after installing sharepoint. You need to know the passphrase for the farm and other farm configurations. I strongly recommend not doing this since sharepoint 2010 is a productiv server. I would suggest you update your Sharepoint 2010 to SP 2013 and then farm creation should be easy. If you can afford it you can create a test enviroment with two servers.