Do you have the animal barn? If so, go through it and check that none of your pigs or horses have prized out and not been auto removed. Also remove any with less than two feeds left to them.
Do you have the Collie dog that barks at fed animals ? If so you may have to put it in Inventory,( most of us have).

I think this is about the feeding trough (not the mud wallow).
I sometimes get that lag after clicking on the trough to feed the stable/pigs. Then I go do something else on the farm and come back to the trough. It shows yellow feed inside the trough but the animals haven't popped up their post-feed items yet. So I reclick on the trough and that usually triggers the feed animation.

All these animation lags are most likely related to available RAM on your computer. This game (and the Launcher) are huge memory hogs. Depending on what other software is running on your system, there could be multiple lags at a time. Also depends on what other animations are running on your farm as well. Those with bigger farms or more moving decorations could be affected even more.

It just depends on whether you have connected to the site by "http" (not secure) or "https" (secure) - you'll see that by looking at the URL in the address bar. It's just letting you know that any data sent between you and the website is not encrypted. For the purposes of the game, I wouldn't worry about it as there is not really any sensitive info being exchanged.

Having said that, the game may be over a secure connection, but the images used can come from a non-secure server and your browser will detect that too.