The clues may have a word to be removed before solving.
14. Professor’s incisive theories implement Archimedes’ Screw? (6)
31. Guitarist shoots up small line (5)
I am assuming that first letters of the extra words can go in either end column.
The last letters in the other column.
I do not see any words forming yet.
I am not sure what to do with extra words from down clues.
Thanks
Yes, the first/last letters from across extra words can go either end, hankir.
The down clue extra words each feature a symmetrical arrangement of double letters - these spell out a hint to the similar symmetry found in the grid.
Yes, that's the park - for the next one you need the long T word for the team + a 4 letter H word for 'robust' (then look at the tube link - the line is given by the name in the diagonal - then somewhere in the middle on the route from the park to TH).
16d a 3 letter word for a pool/waterfall followed by a very obscure 6 letter word for a partition (I'd not heard of it) 'severy' - remove the two letters for '250' and 'roubles' and the extra letter - what remains is an obscure cloth.