Transport to Heathrow on December 23 and security questions

Given this is a busy time, what time should we be at the airport to check in and clear security?

3 hours or more. Your airline will probably tell you exactly this the night before or has it spelled out somewhere on their website. The airline's goal is to leave on time.

How about security check-points? I've read through the requirements for carry ons, what's allowed and what must be placed in checked baggage. Is there anything new that has changed in the last six months as far as security checks?

No. And everything new would be spelled out on the airport website for sure:
https://www.heathrow.com/customer-support/faq

I expect that there will be long delays waiting to get through security.

Usually for transatlantic flights you have to be there 3 hours or more before as others in front of you may have overlooked the rules about liquids that should be placed in the plastic bags supplied by the airport before you enter the security screening lines., thereby slowing down the screening process. Also sometimes there is a 2nd security screening conducted by the airline after or before the first.

Heathrow express would have made no sense anyway. I’d just take the tube Piccadilly Line.

While I have played chicken with the 3 hour check in the past, I wouldn’t do it so close to Christmas. You’ll have the infrequent flyers who haven’t flown since Thatcher was Prime Minister, plus it’s just a very busy time. Heathrow has plenty to keep you occupied and the prices aren’t ridiculous by London standards.

While every year is different, I flew out of Heathrow last December 22nd with a flight time around 11. My hotel was in South Kensington and I took the Picadillly line straight to the airport. It was super easy and took about an hour. We allowed three hours prior to boarding to get to our flight and it was fine. I use the boarding time not the departure time because most flights take 40 minutes or so to board and I want to make sure I can get on earlier enough to get overhead space. The added advantage if there is a delay, I give myself a little cushion.

Tickets are currently available on the HeX that day from £15 o/w. If you really want to go that way

23rd December is an ordinary working day, so public transport should be running as usual. Like Marco I can see tickets available for that day - were you looking at the 24th instead?

If you are travelling from Kensington, I would suggest taking the Piccadilly Line from South Kensington or Gloucester Road to Heathrow.

Keep in mind that some things that US TSA allows to be considered 'medical' items (specifically, contact lens solution, etc) is not considered the same at Heathrow, so those items must be put in you r 3-1-1 bag if you have them.