There ARE NO WD utilities on it anymore, could that be a problem?
No. The utilities have no effect on the working (or non working) status of the drive.
I have a bunch of 4TB, 6TB and 8TB Seagate and WD external USB drives and they all get very hot in use (as in over +55°C). Aiming a large desktop fan over the drives cools them down.
I no longer trust these external hard disks with anything important. For a start they use USB3 and I've had problems with drive communications cutting out due to USB cable length. I now use short (30cm/1ft) USB cables.
When using external USB drives of any sort (HDD and SSD) to back up critical files, I run a byte-by-byte comparison of all files after transfer using FreeFileSync, to check that no corruption has occurred.
On top of that, spinning hard disks can sustain damage if bumped or knocked during operation and I hate to think what would happen if a USB drive toppled over (head crash).
Add to this list the fact that many of these external drives are SMR and not CMR and I've abandoned them as a means of backup. SMR slows things down considerably on "well used" disks. My USB drives contain old archive data which is backed up multiple times elsewhere. I haven't used them seriously for years. Too slow, too hot, too dodgy.
"My Book" WD external HDD that is sometimes non responsive, gives errors and cannot be recognized at times by TV and PC.
The non resposive problem could be down to USB. If your Windows? PC is set to power down all USB Hubs (to save power when idle) then some external devices may not reappear when polled again by the OS. I disable all power saving options for USB in Device Manager.
Many TVs "reformat" external drives, making them unrecognisable when connected to a Windows PC. You may have to reformat a TV drive before it becomes visible in Windows. TVs might use FAT32 or exFAT and some proprietary data encryption. Windows will probably format NTFS. Then of course there's iOS.
As I said above, your USB cables may be too long. Forget the 1m/3ft lead supplied with the drive. Buy something less than 0.5m/1ft6in long.
The drive may be corrupted. Pending blocks, bad blocks, MFT corruption, who knows? It might be on its last legs. Nothing lasts forever.
On a Windows PC, run CHKDSK /F /R on the offending drive.
https://www.howtogeek.com/1033/how-to-use-chkdsk-on-windows/
Consider a full surface Read scan using a trial copy of Hard Disk Sentinel (takes many hours).
https://www.hdsentinel.com/help/en/61_surfacetest.html
You cannot claim a drive is fully working unless you run some serious (time consuming) SMART tests.