1) Please send us a complete set of logs that you can gather by following the instructions in https://www.nomachine.com/AR07K00677. If you prefer, you can email them to forum[at]nomachine[dot]com.
Furthermore, we would like to see a screenshot of the Display settings tab, the one shown at paragraph 5.6 of this guide: https://www.nomachine.com/DT10K00060.
2) Is it the local or the remote host to turn black? Logs of point above can be useful here too.
3) We checked the ffmpeg package of the link in option 2. This pre-built avcodec has also a dependency to swresample-1.dll. So what you need to do is just copy swresample-1.dll to C:\Program Files (x86)\NoMachine\bin and it should work.
You could also use the ffmpeg package we provide here: http://www.nomachine.com/opensource.
Instructions for compiling are here: http://www.nomachine.com/AR09K00690.
4) That warning is not critical and it won’t prevent the software from working correctly. Anyway it will be fixed in the next update.