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Is the New York-Chicago route electrified?
Depends on what corridor you're talking about, since there's more than one. The ex-NY Central corridor (used by the Lake Shore Limited) is electrified between New York City (generally speaking) and the former Croton North station in NY State; the former Pennsylvania RR main line is electrified between New York and Harrisburg, PA. There was another NY-Chicago route, that being the former Erie RR main line, but that was never electrified and it only plays host to NYC area commuter trains and freights nowadays. The only electrified routes in the Chicago area are the ex-Illinois Central Metra commuter lines to Blue Island, plus the South Shore Line (currently North Indiana Commuter Transit District) between Randolph Street Station and South Bend, IN.
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Regarding HSR, i thought that there is a HST between New York/Boston/Washington-Chicago route
There is a HST running between Boston, New York and Washington (not Chicago) on former New Haven and Pennsylvania RR lines, but thanks to some tremendous gaffes, speeds are held down for the vast majority of the route. Nowadays, the service is advertised emphasizing comfort, not speed, since the speeds of the train are matched by the older AEM-7s hauling Amfleet cars.
The former NY-Washington-Chicago train, the Cardinal (cut back to between Washington and Chicago nowadays) always had to change power en route.