Can SoSci.de (the free academic version) do the following?
Except for the descriptive analysis module, the features are the same, regardless if you pay for SoSci Survey or make use of the subsidized service.
Measuring time spent on question more presicely than 1 second
You can do this, using JavaScript, for an introduction, start here: LatencyTimer
The online help suggests that 100ms is possible, can anyone verify that this works, and is more precise possible?
Based on screen limitations, accuracy down to 20-30ms is plausible.
Is it only possible for some question types or any?
A few have the measures included, others require you to write additional JavaScript code.
If there are multiple questions on one page, can I measure the duration of each question separately?
What you can measure is clicks and points. It's up to you to define what the time for a question is. What if question A is answeredm then B, and then the answer for A changes?
Logarithmic slider, ideally continuous, showing the chosen number. Scales would be something like 0 to 10 000
The internal coding will wlays be linear, because this is what the movement is. You can, however, use maths to transform that into a a logarithmic or exponential space and show the respective numbers: Display the Current Position
Two visually bordered sets A and B, presented horizontally, both with three lines of text vertically, the respondent picking A or B.
This will probably require some HTML, for inspiration take a look at these manuals:
I would prefer like the border being clearly bolded or something.
I am not entire sure who you would like the result to look like, but you may post another question (only on this one, please) and include a sketch or mock-up.
Questions made so that separately clicking "next" is not necessary.
You can choose an automatic "next" in several question types, for example in scales and single-choice selections.