@Jens, it looks that you have problem with folder permission. In that case use manual update.
- Download Template or Plugin package
- Unzip
- And using FTP override files from folder: plugins\system\helixultimate
- Then update Database in Joomla
@Johan
In general, yes - most changes are in plugin. But if you updated both you should have 2.2.7.
If you not sure, just install template package, becuase plugin cannot update template.
@Christos
Do you have any firewall component installed? If not, consider that! I cannot promise you fixes for old versions. But tomorrow I will talk with our team what we can do for J3 users.