A cart can be pushed to the monorail door. I am not sure about carts when you arrive at Hamamatsucho. We travel with a backpack and one small rolling luggage even though we are in our late 60's so carts are not what we look for, but I don't remember any. Should be a great trip.

the Haneda Express goes without stop to Hamamatsucho. real easy. then get on Yamanote and get anywhere.

it's including. you can use ur ticket for the monorail at airport

I suggest you buy a Pasmo Card, which you can use across Tokyo rail travel (except possibly shinkansen, not sure) plus bus plus taxis. You can get your pasmo card at every station instantly. This way you can swipe thru your travel without hassles.

My advice is much the same: Take the monorail to Hamamatsuchou (the last stop) -- the Monorail is faster and much less expensive than a cab, From Hamamastuchou, you have the option of a cab or a direct connection to the JR Yamanote Line (direction Tokyo, change one stop later at Shimbashi, follow signs to the Metro Gnza Line, then take that to Toranomon.). However, at this hour, the best bet is probably to grab a cab at Hamamatsuchou. There are always cabs waiting there -- take the elevator down after you are through the fare machines and the cabs are right outside the door. The cab will take you right to the door of the place you are going - be sure to have a written address. The cab ride is about six minutes and will cost about 1500 yen, maybe a bit more, to Toranomon. At Haneda you might want to buy a Suica card from the machine (you can push the "English" button of your Japanese is not so good) and then you can use that card to pay for all JR trains, Metros, Taxis, and most convenience stores and kiosks. It's incredibly useful, you can recharge it as often as needed, and get a refund for unused balances (minus 500 yen) at the end of your trip (or save the card for the next visit, better still.)