I think these are correct but would appreciate help with parsing......
1a. On a spring day, somewhere to sleep in the shade (7) - APRICOT (Shade) If 'Somewhere to sleep' = COT then why is APRI 'On a spring day'? It's almost 'April' but there's no instruction to cut it short , so I'm at a loss.
16a. Worldly city not quite safe to be around (7) - SECULAR (Worldly) I think it's SULAR around EC (City) so presumably 'Sular' is 'almost' a word meaning 'Safe' but all I can see is 'Insular'.
18a. Draconian censor awarded many medals, possibly for song (3,4-8,6) - THE STAR SPANGLED BANNER (Song) Other than 'Censor' = BANNER I'm at a loss.
40a. Exhausting to be in the city? On the contrary (6) AUSTIN is hidden - exhAUSTINg but why the ? and 'On the contrary'?
57a. Vessel in heart for one, say, going on to beat (7) - TANKARD (Vessel) I see TAN = 'To beat' but not the rest.
26d. Are in the West, presumably, to take in Grand National (9) - ARGENTINE (National) Other than 'G' for 'Grand' I'm at a loss.
34d. Mystical bit of conjuring almost conceals a holy text (7) - TANTRIC I think 'Conjuring almost' = TRIC(k) but that's as far as I get.
46d. Ingenious tip for practice set up worker (7) ELEGANT I get as far as 'Worker' = ANT but that's it.