Richard, they mean to literally behead the plant (knife or clipper), at which point you will have a short stem sticking out of the soil and the top part of the plant with some stem. Don't leave that stem too long. Let that top part harden off over a period of days or more, in other words dry very well, and then stick it back into soil so it can grow new roots. You can search how to root a cutting, which is what you will be doing.

Roof looks great with your brick! I'd follow suit with the windows and get windows with no grids that have bronze frames. (picture below just for frame color reference). For your door I think you could save your door if you're able to replace the ornamental glass insert with a simple one and paint it a bold color that compliments your brick. Otherwise a new mildly contemporary door with cutouts. Definitely remove the teal planters as their tone does not go with your brick. Some simple landscaping with perennials and shrubs underneath the windows would be very pretty. Where is the street in relation to the front of the house?

I don't, but if you click on the link that says "More Info" below the photo, you'll see which pro posted it on Houzz. You could then message them to ask whether they still have the color/brand on file. I would bet money that the Benjamin Moore store could find you a sage green in their Historic Color palette that is very similar.

https://www.houzz.com/products/query/drum-side-table/nqrwns Here are lots of drum side tables. The rug should be big enough to slip under the front 1/3 - 1/2 of the sectional and extend past the right and left ends of it by a foot or more. Use blue painter's tape on the floor to tape that out, then measure and buy a rug in the closest size to what your taped rug measures.