[noggin]

If I plug my nvidia shield on the hdmi on my Lg Oled and I watch a movie with Kodi in true hd 

1) Can kodi convert the signal to DD+ ? so my tv can send yo my soundbar  ARC

Not DD+ - but you can enable transcoding to DD. Configure Kodi for 2.0 output (unintuitive I know), and then a 'transcode to Dolby Digital/AC3' option appears under the DD/AC3 passthrough switch.  This will allow you to transcode 5.1 FLAC, AAC, PCM etc. audio to 5.1 DD.

2)Can Kodi convert DTS HD to DTS?

No - but most (all Blu-ray) DTS HD content contains a DTS core - so that is bit streamed instead. (DTS HD as used on Blu-ray consists of a DTS Core signal + a DTS-HD 'add on' that contains information that can be added to the DTS core to create a loss-less output instead. (There is technically a version of DTS-HD that doesn't have a core I believe - but I don't think it's seen 'in the wild' much as DTS-HD is sourced from Blu-ray rips, unless people have mastered it themselves)

4)Kodi can read all type of sub on 4k mkv ??

I've not found any subtitles that Kodi can't handle yet that are in the mkv wrapper spec (or external) and I've not found them to be resolution dependent.