trying to figure out how many ribbons i need to ordered, how many stickers (RL936TT) does 1 ribbon do?

The TR2181ZW has a length of 243', 2,916". With the height of the RL936TT label being 1.5" (plus 0.125" for gap), you could potentially print 1,794 labels of the RL396TT using one ribbon.

is this compatible with the zebra ZD420T - label printer?

The TR2181ZW is 4.33" x 243' which meets the ribbon specifications for Zebra's ZD420T.

Does this ribbon's core have slots cut into the core as pictured? (When I use it as the take-up core, it needs to have slots to attach properly - Intermec PC43T.)

Yes, for our 0.5" core thermal ribbons there are slots cut into the core.

Will this prevent any smudging if I were to rub on the label when trying to apply to product?

Our Durable Wax (ZC) Resin thermal transfer ribbons are recommended for use with our synthetic weatherproof materials. These provide high resistance to scratching and abrasion while applying and while in use.

what color are the ribbons?

Our thermal transfer ribbons are black. You can review our Thermal Transfer Ribbons page at the link below for more information and to view our available sizes. https://www.onlinelabels.com/thermal-ribbons.htm

Does it come with the take up core?

Our thermal ribbons do not include an additional take-up core.

I just purchased this thermal ribbon for a Zebra TLP-2844. I saw in an earlier question that your ribbons do not include a take up core. Based on a video I watched I need that to install the ribbon properly. Is the ribbon I purchased not able to be installed as is? If not, where do I get a take up core or ribbon with it included?

New thermal transfer printers will generally provide you with a take-up core to get you started. I would reach out to Zebra to see if they can assist you with this. Moving forward you can use the empty core from the previously used ribbon.