Train Schedules in England

https://ojp.nationalrail.co.uk/service/planjourney/search

You will probably find that many dates may not well have been loaded on to the system yet, especially at weekends. They will come, you're just too early. You can get an idea of the schedules and prices by looking at dates in late August and early September.
Stonehenge can be accessed by a train from London Waterloo to Salisbury, from where you can Cath a bus to Stonehenge. this is an easy day trip with time to look round Salisbury as well.
By "The Wall" do you mean Hadrian's Wall? If so that is wholly within Northumberland and Cumbria, not Scotland.
It would be good to give us a rough idea of dates and more exact journeys, as then we can give you more detailed advice.

The general schedules are good from May to December- what isn't in the system yet are any changes due to engineering works. Depending on the railway line those are announced 8 to 12 weeks ahead of schedule.
Usually such engineering work only affects weekend travel.
At least for Hadrian's Wall the Newcastle to Carlisle railway engineering works and advance tickets are released at 0001 exactly 8 weeks before travel. Full priced tickets are available before then, but the times are subject to change. Northern (for that line) have recently introduced a hugely expanded range of advance tickets. They are well worth while waiting for as some of the prices are astonishingly low- Northern Advance tickets are available until 5 minutes before travel (that is not theory, they really are). There are now advance fares for journeys as short as 8 miles.

For the Hadrian's Wall line see timetable N4 on this web page.

In the rest of Northumberland (on the East Coast Main Line) there is no unified printed timetable-
trains are run by Northern (see timetable N1 on the above page), Lumo (calls at Morpeth), LNER, Transpenninne Express and Cross Country Trains.

Oh, and by the way, Cumbria no longer exists- abolished in May 2023. The western part of the wall is now in Cumberland.