So you have two issues here.
The first is that the new user you created cannot create a new dir. This is because, even though you’re changing users (user → root → user1), you’re still in the home directory of user, which user1 can’t write to. What you need to do is either specify a user directory when you create the user, (useradd -d /home/user1 user1), as @fedorqui mentioned, or, if you’ve already created user1, use the usermod command to add a home directory to user1, like this:
usermod -d /home/user1 user1
If /home/user1 does not exist, you’ll need to, as root, do the following:
chown -R user1 /home/user1
What this is doing is first creating the directory, and then assigning ownership of it to your newly created user. So now, when you do su - user1, you’ll end up in /home/user1. You should now be able to create directories and files.
Your second issue, “user1 is not in suboers file.”, is a result of how sudo manages which users are allowed to use it. The rules that control this are in /etc/sudoers, which you should edit with visudo. If you wanted to allow user1 to run whatever they want with sudo, you could add a line like this:
user1 ALL=(ALL) ALL
Which says that user user1 may run any command on the system as root. If you now try to run a command with sudo as user1, it will prompt you for user1’s password and then run the command.