Electrical – Do I need junction boxes where conduit containing data cables terminates

I take it you're hoping to poke sticks of conduit up from the basement and hope to come out in the attic without hitting anything? It could happen, but I'd be rather surprised. 1.5" conduit is fairly chunky, I think you're likely to hit something. If you wanted to fish a few runs of Cat 6 I'd say your chances were good. But conduit? (BTW, bonus points for knowing better than trying to run inside the duct.)

Even if there's obstructions, it may be possible to make the run by cutting discrete access holes to cut out the obstructions, assuming they are non-structural. If you haven't yet done so, examine each floor carefully to determine if there's enough space to even make the run. Measure carefully to arrive at accurate void dimensions, and ensure the proposed run aligns on each floor, which may not be that simple. Once you've determined it's feasible, start pushing pipe, keeping track how much length is pushed up. You'll likely hit something. Figure out where it is vertically. Gain access and clear the obstruction. Repeat as necessary until the attic is reached. Good Luck!

You will need to refer to the documentation that came with your new appliance. Is it rated to be connected with a cord an plug or directly wired?

To start with you will need to run a new cable of 10 gauge wire and replace the circuit breaker in your panel. Operating the appliance with 12 gauge wire when it is rated more than 20 amps and requires 10 gauge wire violates the manufacturers instructions as well as overloading the circuit.