Yes, a table would be fine on the wall next to the door, especially since the door opens the other direction. Just make sure it isn't too long to be in the way of what I assume is the coat closet. You can try your wicker bench under your mirror and remove the dried arrangement.

Move the bench under the hanging item and remove the wreath and dried stuff. Shop for a rug at ruggable.com - washable and lots of styles.

any suggestions on what to put in these two spaces?

You can put a dresser\cabinet there to store keys, gloves, hats, umbrellas etc that you need to grab on your way out the front door. Do you bring the mail in the front door? A hidden recycling basket or bin you can immediately toss the junk mail in, and quickly sort the rest. Since it’s your front entry, I would avoid hooks or anything that will attract clutter or mess.