Why Steam doesn't like external HDDs?

It's because USB slows the transfer speed compared to an internal drive.

If the game requires lots of reading/writing to the HDD, it will have take longer to load and potentially even cause freezes. Other games will work perfect without you noticing anything.

I have my steam on my external and I don't notice much if really any loss in performance. If it worries you I would suggest connecting the external via USB3 as it will be the fastest. eSATA next and USB2 last if the options exist for you. One issue I have is I launch Steam directly from the .exe in the steam folder on the external since there is the possibility of drive letter change. If you want your massive steam library (mines 1TB right now) to be mobile or don't want the hdd running when not in use then external is great. Transferring is easy, step 1: copy or move existing steam folder to external. step 2: ? Step 3: profit!

yes, don't use a usb drive to install games, if you really want to put games on it, remove the casing and plug it directly to the motherboard via the sata port, you will get better performances an you will reduce greatly the risks of failure.

If you have a desktop PC with a little space inside, there's no reason you can't disassemble the caddy and plug the drive into a regular internal SATA port as an additional drive.

It's a good idea to move your data files to the external hard disk instead.

Many external hard disks aren't good desktop drive, but they are great just as storage drive.