from Davinci to Premiere Pro almost-missing images, missing nested sequences and missing any titles.

This is a good question for the DaVinci resolve basic forum. The user manual is also stunningly good and Command F (Ctrl-F) works wonders when used in the Adobe Reader.
Resolve will not understand NLE timeline fully. That being said make a new assembly that has all of the video clips and edits on one track of the timeline all of the stills on the other and all of the titles above it. Open up nested sequences and put the clips onto the video track. You then may disable video track and output stills track as a video, title track as a video and reassemble with the clean video XML track in resolve if you must grade titles and stills together with video.