The doctor has lost his sonic screwdriver before and has made a new one - he's probably got a stock of them in the Tardis by now.
Susan is the doctor's grand-daughter, who was the means of introducing the doctor's first companions , Ian and Barbara - they were her teachers at a school she had persuaded her grandgather to let her go to - she was apparently about 15. They were curious about why she knew so much about some things - science etc and so little about others - eg she thought Britain already had decimal coins in 1963. They followed her home & discovered that 'home' was the Tardis.
In the second series, they came to Earth in 2164 & found it had been invaded by the daleks, who had first reduced the population of Earth with some kind of plague and were now mining down to the centre of the earth (starting in Bedfordshire for some unknown reason) with the intention of replacing its core with a drive system so they could pilot it around the universe.
A lot of the population had died, more had been turned into Robomen,who controlled the
survivors being used as a slave labour force to do the mining.
Anyway, to cut a long story short, the Doctor foiled the plan with the aid of a band of freedom fighters and then discovered Susan had fallen instantly in love with one of them in the usual way of the Doctor's companions who need to be written out.
So they were left in london in 2164 and may very possibly have had children, who are half Time Lord, half human and therefore the Doctor is still the last Time Lord, but he's not alone because they would be his great-grandchildren.
Of course, there is also still Romana, who was a Time lady companion to Tom Baker and was left in ESpace, so may possibly return....