Now that I've shot my mouth off, I feel obligated to answer some of your questions, though because of the complexity of the subject, this site is not the place for such detail. Forgive me if I have come across as one of those from a different forum who has to have the last word and is negative about everything. That is not my wish or goal.
You are correct that your rifle has many features that are similar to rifles from the Hawken shop and I can see how one might draw comparisons. It has been suggested by some students, collectors, and builders, that Hawekn rifles borrow heavily from English sporting rifle tradition, ie: scroll shotgun style trigger guard, captured double barrel slides, escutcheons around the keys, patent hooked standing breech tang and plug, percussion snail bolster and nipple seat, sheet metal under-rib and rod thimbles, beavertail cheek piece, and so on.
But generally, Hawken rifles have heavier barrels and larger calibre, sheet iron or cast nose piece, plain maple stock wood, two captured barrel slides with iron escutcheon plates, gentle purch belly to the underside of the buttstock, simple scroll trigger guard, less definition around the lock panel, iron lock bolt escutcheon, entirely different percussion lock plate, deep crescent iron butt plate with less of a heel extension.
Hawken rifles and your fine piece, are almost contemporary. I suggest though, that your rifle antedates the Hawken mountain rifle, and I feel that Mr. Beck, the maker, did not draw heavily if at all from the Hawken design. Percussion half stocked rifles of the middle of the 19th C, in North America, I believe were far more influenced by English and even Continental firearms, many of which were being imported and sold in gun shops and hardware stores across the continent, in competition with the hundreds of American gunsmiths who were turning them out by the thousands.
I and many others who frequent this site, have invested a lot of money and time in order to study particular styles, and get it right when we replicate or re-create these interesting firearms. So as Eric has so acutely and gently has said, it is just an old geezer nit-picking when someone throws out a catch-all phrase such as "Hawken styled" to describe your wonderful rifle. Thank you for posting pictures of it.