Hi, your Hawthorne De Luxe has a serial number beneath the bottom bracket - if it's anywhere near H18000, it's probably post 1918 - 1920. The frame design was introduced in 1914. It is not the Flyer model.
Your first photo's handlebars are almost correct but should be mounted up, not down. The seat pin is wrong - it should be a 7 style. The wheel rims are wrong - they should be Lobdell section either wood or steel clad wood for single tube tyres.
The chainring should have "hearts" - similar to the Fauber one [see Chainwheel Tattoo Project on Google]
I have all the correct parts, the handlebars, stem, truss rods and guide bracket, the complete - headset cups, nut, washer etc., the seat pin and I have the complete crank axle, chainring and cups, lock rings etc. These have all been parted-out and are ready to go to the re-platers. Your frame should have a white head-tube with white darts on the adjoining tubes, similar darts on the top of the forks and a white panel on the seat-tube with pointed ends. There should also be a small Patent decal, back of the top-tube. I might be tempted to part with all the above items, but they cost me a lot of US Dollars to buy and ship over to the UK - and to be fair, they are extremely rare items.
Regards, Keith
The badge should have a blue rim with the words Hawthorne De Luxe inset, the centre section should have a female form above a "world"