You can edit another file while capturing (if your system is fast), but you cannot edit the file you are capturing. If you set your file capture size down to just a few gigabytes, you could start editing within just a few minutes of beginnning the capture.

timecode in picture is just a small timecode window inserted somewhere in the preview picture (a picture in picture). You need it to help an offline speaker.
The dual stream is needed e.g. for live slow motion. You cannot stop recording while you play the slomo.

To display the timecode, there might be an additional hardware-clock that displays the midi-timcode. If that exists?

saxofon,
what you need are realtime broadcast type tools.
You needed a dedicated slomo replay system. This is usually separate to the system recording an event, after even the best tape drives cannot keep recording and rewind to play out a segment.

VV can generate burn in time code as an effect, if you can afford the time to render out and then play the segment fine but I suspect this is not quite what you want to do.

Probably you want to be able to play a tape out withour displayed time code and have a separate feed with timecode displayed. To do this you'll need a time code reader which will insert the time code into a feed as part of the video. Ideally you'll need a VCR with dedicated TC output.

Expect to pay BIG dollars for this kind of gear, anything that works in reatime need lots of hardware and/or has a limited market.