1) If I just want to upload photos (without text) then it tells me that I have to enter some text ("Please provide a message.")... That is somewhat annoying and can defeat the point.

You can't post activity without submitting a message. That's a limitation of CB Activity and CB Gallery can not override it. Have added a feature ticket to CB Activity to see about implementing message-less posts as long as some other content is attached that is meaningful (e.g. location, mood, upload). Sharing photos with no message can just be done from CB Gallery for the time being.

forge.joomlapolis.com/issues/6709

2) try to upload using a mobile, you can only upload single photos and this can be very annoying...

It uses a standard file input and allows multiple file selection. It's up to the mobile devices to be compatible with this. There are no plans to implement a heavy JS library to support this specifically on mobile.

3) When I click on the photo, it shows me a black screen including an error message: EDIT: Only seems to happen when a CB moderator clicks on that image... The normal user works perfectly fine. EDIT EDIT: The user cannot click on his own photos inside ACTIVITY.

After it has been saved? After the page has reloaded? After upload in the upload preview? Where are you seeing this exactly. All 3 cases seam to be working fine in my tests.

4) The CB gallery resizing before upload is dearly needed. I barely can upload photos over mobile...

Client side resizing is planned as noted below. No idea if it works on mobile though, but suppose it should depending on the capabilities of the mobile browser.

forge.joomlapolis.com/issues/6228