Timecode is the issue as Media Composer AMA linking is not reading the timecode in the file. You might want to consider creating native Avid Media in Resolve to ensure timecode is correct. Be sure to set up REEL ID correctly. Also, the free version support 4K UHD (3840×2160), not 4K or higher.
As far as the second issue, there is not a lot to go on without seeing it or having the file to test with.
You may want to invest in the Nablet XAVC-S AMA plug-in for $99 if you want to do transcode in Media Composer.
https://www.nablet.com/products/plugins/avid-media-composer/xavc-s-ama-plugin/
Also, DNxHR LB is not 1080 unless you are working and transcoding in 1/4 proxy while in a 4K (UHD) project. Also, note that DNxHR 1/4 proxy is exactly the same as working in DNxHD 36. Now if your aspect ratio is not 16:9 for 4K UHD, then work in 4K with 1/4 proxy.
Michael