jenak1998,
Beautiful Dayton, not many survive in that nice a shape. Your correct, it is a model H, Underfeed rather than Vertical Feed. 1901 is a good estimate on it's date as I've never come across a dated warranty for this model. The warranty card probably would have been a page in the owners manual and filled out by the owner. The first Davis Underfeed, the Advance, model E was introduced around 1892, shortly after Davis moved to Dayton, Ohio from Watertown, NY.
The most common available needles for the "Davis Long" is the Boye #10 and MTx190. The Boye #10 is a new old stock wooden tube with three sometimes 4 needles that would have been sold in hardware or general stores. Cost is around $10 per tube on ebay. MTx190 is an industrial needle with the same dimensions as the Boye #10 but with a round shank instead of flat. The MTx190 needle must be aligned so the scarf is to the right and the long groove to the left for the machine to sew properly. Cost is about $4 for 10 on ebay.
Here's a manual for a Davis Burdick, model G, slightly smaller sister to the model H.
http://www.sil.si.edu/DigitalCollect...f/sil10-37.pdf
Enjoy,
Jon