Couple Practical Questions: To/From Bath + Salisbury and Stonehenge

1. Basically yes. You will pay a higher price for the ticket but I think it is much smarter to buy that ticket on arrival. Lots thing can go wrong so reducing your potential stress is always smart.

2. It has been years since we did that loop but I think you are trying to do too much. But I let some with more current experience comment.

emphasized textHoping to get to Bath to Stonehenge and then back to Salisbury for lunch is very optimistic...

Train from Bath to Salisbury takes about an hour. Buses for Stonehenge leave Salisbury Station on the hour, with the first bus leaving at 10.05, getting to Stonehenge at 10.40. Being realistic you probably need to allow AT LEAST two hours+ to visit Stonehenge. It is quite a walk from the visitor centre to the stones (although there is a shuttle bus). and there is quite a bit oif information in the Visitor Centre exhibitions too.

Buses leave Stonehenge back to Salisbury at 5 minutes before the hour but return via Old Sarum, getting back to Salisbury around half past. You might make the 12.55 back to Salisbury for 1.30ish.

Allowing for lunch (either at Stonehenge or in Salisbury) could take another hour depending on how busy places are - unless you are grabbing some sandwiches.) That could take you to 2.30 for a visit to Salisbury Cathedral. It is recommended to allow at least 1.5-2 hours here especially if you want to see the Magna Carta.

That will give you a bit of time to explore some of Salisbury. It is doable but you will need to keep a strict eye on timings...

The way the smart traveller does it is to get a bus #272 to Devizes at 0745, then another one to Stonehenge, the X2, arriving there 45 minutes before the first tour bus from Salisbury at 0949, then the 1159 X2 to Salisbury arrive 1223.

But yes a ride share/taxi is another alternative.

Then train back to Bath.

To York (leaving from Kings Cross) there are always walk up cheap Advance Fares available until 2 minutes before each train departs, so just buy a ticket on arrival.
All long distance Advance Fares come with a seat allocation, even one issued that late

The Heathrow express terminates at London's Paddington station but York trains depart from London King's Cross, about 3 miles away. So don't hang around Paddington, take a tube, using the Hammersmith & City or Circle lines, it's only 5 or 6 stops. Each of you tap in and out of the tube using your debit/credit cards.
I can see York trains in the next few hours as cheap as £57 and as high as £148. If you pay more than £105, buy a Two Together railcard for £35, which will give you a 33% discount on off peak trains and lasts all year, so handy if you intend making more train journeys. What will be your rail departure time, and which day of the week?
Tickets and railcards can be bought and stored digitally on your phone, so you can load and use the rail operator app, LNER, same with the Railcard app, you'll just need a couple of photos in your phone gallery.
If you decide to buy a paper ticker from a booth, make sure you look at all the train options as you might save a lot of money bu simply waiting less than an hour for a cheaper train.
For future information, there are alternatives to getting from Heathrow to London. As well as the Heathrow Express, there are the Elizabeth and Piccadilly Lines, which will be cheaper than you will have paid for the HEX. The EL is very modern and uses someof the same track as the HEX, the Piccadilly line is older but can be as low as £6 for that journey and has the advantage of going direct from Heathrow to Kings Cross, no change required.

1- I would wait and buy on the day- tho it will be more expensive, it's hard to know exactly when your flight will arrive. As mentioned below you will need to get from Paddington to King's Cross for the train to York.

2- This is absolutely possible. I have done pretty much this exact itinerary twice, and from London which is further from Salisbury than Bath. If you are looking for somewhere to eat I would check out Haunch of Venison, which is an extremely atmospheric and haunted pub in Salisbury.

If the OP has got an Advance ticket for the Heathrow Express, then even adding the tube fare on, the Elizabeth Line would have been more expensive, by nearly £3 (and taken longer).
Although with a railcard the Heathrow Express Advance Fare would have been only £6.65 each.