Real bananas will not work in this recipe well. The cookies will have a completely different texture and the icing recipe won’t work, it won’t set up correctly.
Here are some recipes I have that do use bananas
https://www.createdby-diane.com/2014/05/brown-sugar-banana-nut-muffins.html
https://www.createdby-diane.com/2013/06/oatmeal-cinnamon-banana-cake.html
https://www.createdby-diane.com/2014/09/banana-bread-pudding-with-caramel-sauce.html
https://www.createdby-diane.com/2014/01/peanut-butter-banana-bread.html

It could be the spatula, I would suggest a thin metal spatula (the newer silicone spatulas don’t let the dough come off of them easily) I’ve even used a small offset spatula, the type you frost cakes with. they are super thin and release cookies well. A regular sized offset spatula would work as well (the type you frost cake with) If you are rolling your dough onto a wood surface, be sure it is lightly coated with flour or roll the dough between sheets of wax paper, that is what I have been doing for while now and find that trick works really well. I typically don’t have any trouble rolling this dough out. If your dough was too sticky, roll the ball of dough in a small amount of flour so it doesn’t stick as much. The texture shouldn’t be sticky. This dough is smooth. Of course there are a few things that make baking differences: temperature of butter, the warmer it is the stickier the dough is. Sorry to hear you had trouble with the dough. I’d try rolling it in between wax sheets and see if that helps.

Thank you so much for your reply. I forgot to add that I had trouble with the dough coming off my spatula to put on the sheet pan. I ended up dipping spatula in flour and that work for 2 cookies then had to re-dip. Sometimes the shape was lost scooping them up. What am I doing wrong?

They have great flavor and taste well for a month at room temperature wrapped individually. If they are in a container that does not have much air (empty space) they will last a month. I have frozen them in zipper plastic bags with the excess air removed for a month and then thawed at room temperature. I have not frozen them longer, nor have I had them last on the counter past that time. Just be sure the cookies are completely cooled and icing dried for 24 hours before wrapping or the moisture inside the cookie or icing will be too much moisture in a air tight container or bag (in the freezer it will get freezer burn) If you flood the tops of the cookies with icing, let them dry a minimum of 24 hours. They won’t go stale as the icing will prevent that. Hope that is helpful. If you are planning for Christmas, I think I would make and cool the cookies 24 hours with a sheet of wax paper placed over the tops loosely while they dry out a bit, then place them in zipper freezer plastic bags with air removed (use a straw and such out the excess air) then thaw and ice them when serving.

I am making your cookies right now. How long will they last in an air tight container (not that they will last long around cookie lovers), but I was thinking about making ahead for Christmas.

The cookies can be stacked when the icing in completely dry (I usually wait 24 hours before stacking them) no I don’t refrigerate the cookies. They stay fresh if they are wrapped or placed in an airtight container after the icing has dried for 24 hours.Check them, if you live in a more humid area) If you put them in the container too early there will be too much moisture, so make sure the icing is completely firm.