Tube with teenager, visiting parliament, pub near Buckingham Palace

1) I’d suggest just getting an Oyster card for the teen. Another option might be to use Apple or Google wallet if she has a phone and you can load one of your cards onto the phone.

2) The info is here:
https://www.parliament.uk/visiting/visiting-and-tours/watch-committees-and-debates/

Getting your teenager an Oyster card is easy. You can do it at the airport when you arrive. A staff member for the tube can put the young visitor discount on the card, and then you just add money to it as necessary.

Pubs near Parliament square and the Palace:
Two Chairman
The Feathers
Westminster Arms
The Star Tavern
Horse and Groom
Three Crowns

Believe all serve food. Two Chairman is small. Horse and Groom in Mews.

I would do the sums to see if getting an Oyster card is worthwhile. How old is the teenager? If she is 16 or over she will be charged as an adult, but between 11-25 she will pay half price if you get an Oyster and ask for the Young Persons Discount to be added.
But for a weekend it still might not be worth the hassle to get an Oyster given the non-refundable £7 fee. Does she have a smartphone? (teenager, silly question!). If so, you could link your card to her phone and she can use that to pay. But be careful that she then doesn't take off to Primark!
On the other hand if you do get an Oyster you can then keep it to use in any future trips to London. And it wouldn't have to be used by your daughter, anyone could use it - any discount drops off after 2 weeks.

the credit card doesn't have to be hers, just everybody going through the gates (at both ends) needs an individual method of payment in their hands, and passing one around doesn't work. One active trip on any method of payment at a time.

Could even be one card if different method - so one can have the card, one a phone with apple pay, another a phone with google pay, one a smartwatch, etc. The possibilities are many.

But, sure, you can lend her a card, you use a different card and your spouse a third. That works too.

For daily capping to take effect each person needs to stick with the same method and underlying card all day.

If you go to parliament.uk and drill down through visit, tours, watch debates and committees to the attend debates page, you’ll find information on watching. Generally you don’t need a reservation, but certain meetings do require them. There is also a link to a calendar on that page that will let you know what’s going on the day you want to visit.