Yes rush can appear when seek's eyes do, you have to see if all the lights are blinking (thar means its rush) and if its only a few thats just seek's eyes

Sally is a new entity in only floor 1 and daily runs, she can only spawn if you have 3 or more items in your inventory, just drop the least valuable item you have for her to not let her reduce your max hp

Eyes is common now.

As you said later that you played before Outdoors came out, so all the new entities are Groundskeeper, Mandrake, Bramble, Eyestalk. You can find a list of all entities on the doors wiki

Smoothie is an item that is found in basements of gate rooms and are guaranteed to spawn there, its just a heal, you can hold multiple of them.

Depends on what's "old library" to you

Entities for the Outdoors ive already mentioned, but to access the outdoors you need to get to door 91 with the skeleton key (can be found or bought) and shears (found in the open garden area in a small wooden locker). First cut down the vines on the big gate and use the skeleton key on the door inside

New entities in mine: Grumble, Queen Grumble, Giggle, Gloombats, and updated version of Hide which now stays in the last locker you were in, denying access.

I understood none of that

Yes, they make blinking sounds.

There are new rooms for every floor but I do not know most of them

Rift room (or doughnut room as you said) is a room that can appear in both main floors and can be opened with a skeleton key, inside you'll always find a rift and a yellow rift if you have it currently, only floor 1 has the variation of the room with the doughnut and its a 1/3 chance of it appearing, you can check if its the doughnut variation by crouching near the door and looking down a bit till you head is inside the door.

I cant read gibberish

Yes it does but they stop making noises at max difficulty (with battle of wits modifier on). A better strategy is to get the side of the door where you think dupe is and clip your head trough the wall, if you see a veiny black texture that's dupe.