" Also, I wanted to buy a railway 7-day travel card to use for the 2-for-1 deal. What is the best way to get this card and use it to travel to the hotel?"
You cannot buy the 7 day travelcard with the National Rail logo at Heathrow. So, if you want to use the 2 for 1 deals with a 7 day travelcard, you can get to your hotel by any method you like, then buy the card at King's Cross or St. Pancras stations. (Note that there's no "e" in St. Pancras).
As for how to get to from LHR to your hotel, you can take the tube, but it will require a change. If you want to do this, ask here for which station is the easiest to change in, and if there are any tricks. For instance, at some stations it's easier to go up almost to the exit and then go back down; this actually involves less walking or no stairs, compared with following the transfer signs in the station.
You can book a car (I don't know about Uber, but Just Airports is often recommended); this is cheaper than using a black cab at the airport. This is obviously easiest, particularly if you're jetlagged, packing heavy, have any mobility impairment, etc.
If you take the Heathrow Express or Heathrow Connect (slightly slower but much cheaper than Heathrow Express), you then have to get from Paddington Station to your hotel; this adds cost and hassle, and I'm not sure it's worth it vs. the alternatives, particularly for more than one person (the cost of two train fares plus a cab equals or exceeds the Just Airports cost).