From your logs:
May 13, 2018 10:15:38.303 [0xe3bffb40] INFO - Network Service: Abandoning browse socket, it was closed.
May 13, 2018 10:15:55.800 [0xe2623b40] ERROR - [Transcoder] [mp4 @ 0x9204340] Application provided duration: -1 / timestamp: 155496 is out of range for mov/mp4 format
May 13, 2018 10:30:56.879 [0xf3f24780] WARN - [FFMPEG] - Could not find codec parameters for stream 7 (Attachment: none): unknown codec
May 13, 2018 10:34:03.884 [0xed335b40] WARN - Held transaction for too long (../Library/MetadataItem.cpp:7176): 0.140000 seconds
May 13, 2018 15:25:09.069 [0xef223b40] ERROR - Unable to find client profile for device; platform=webOS, platformVersion=3.7.0, device=, model=49UJ635V-ZF
May 13, 2018 17:37:13.056 [0xe0fffb40] ERROR - Throttle: timed out trying to read chunk 1
May 12, 2018 18:31:50.244 [0xed111b40] ERROR - [Notify] Failed to add watch for /volume4/Plex_vol_4/Series/Altered Carbon/Series (13: Permission denied)
May 13, 2018 19:19:39.302 [0xd1511b40] WARN - Got a transcode session ping without a session GUID (or with an invalid one).
Wow, you certainly have a mixed bag with missing profiles, damaged media, slow database, an app not communicating properly and file permissions issues.
The first thing to do would be to reboot the modem/router and anything connected to it, including any wireless devices.
Then give your NAS and the TV static IP addresses or if your router supports it, use DHCP Reservation.
Then, I would check your media for errors. See Q17 and Q28 on the Synology FAQ's page, link in my signature.
After correcting your media, see Q18 on the Synology FAQ's page and RESET your file permissions, link in my signature. Also make sure the Plex shared folder has R/W permissions for both admin and Plex in DSM Control Panel > Shared Folders.
After taking care of your damaged media, you should re-install Plex. Then follow one of the two proceedures here:
Repair Database: https://support.plex.tv/hc/en-us/articles/201100678-Repair-a-Corrupt-Database
Restore Database: https://support.plex.tv/hc/en-us/articles/202485658-Restore-a-Database-Backed-Up-via-Scheduled-Tasks-
Or simply delete Plex completely and start over. See Q7 on the Synology FAQ's page for more details, link in my signature.
It may also be advisable to reinstall the Plex app on your TV.
You should also update DSM to 6.1.6-15266 update 1