Yes

No, despite the funny [beep] answer you got - seems that these are bike tyres (pedal bike). Might be nice to include that in the title (let alone the description).

Almost certainly - yes. Just check they are 700 x 35. May need new tubes though. Be aware that 23, or even 25 (both quoted so unclear which it is) are VERY narrow for your type of bike. The really are aimed at 'road' (aka 'racing') bikes. I have 28mm on a flat bar Specialized hybrid/fitness bike similar to yours and really wouldn't want to go narrower.

Try a pair of continental GP 4season - not cheap at about £50 a pair but my I've managed 4.5k miles of commuting on typical

Go for gatorskin hardshell

I use Michelin pro4 endurance, thousands of care free miles

Conti Gatorskin/hardshell if you don't want to puncture but are willing to sacrifice grip.
If you want a good level of grip and don't mind the odd puncture here and there (talking 1 puncture in thousands of miles) then Conti 4 Seasons, Michelin Pro4 Endurance or Schwalbe Durano are all great tyres.
More grip, less puncture protection and weight - Michelin Pro4 SC, Conti GP4000s (I'd still say you're unlucky if you get more than one puncture for every 1000 miles with these even in winter).

If you buy cheap tyres like these Conti Ultrasports, Vittoria Zaffiro/Rubino and Michelin Lugano then you probably will puncture a lot, or the tyres will have such awful grip that you won't want to use them. I've never understood why people skimp on tyres, they're your only contact point with the road and last for thousands of miles so it's not a regular expenditure.