I guess the chiral code looks for the following conditions, is an atom Sp3
and are there four different neighbours ("ligands").
> I did not expect these sulphur atoms to be considered chiral.
They are Sp3 and have four different neighbours, one is a lone-pair. Some
tools restrict the case to only a double bonded oxygen (e.g.
https://en.wikipedia.org/wiki/Sulfoxide). InChI for example will also
consider them chiral - you'll need to force the display of unspecified or
assign them.
InChI=1S/C14H14S2/c1-15(13-9-5-3-6-10-13)16(2)14-11-7-4-8-12-14/h3-12H,1-2H2/t15-,16-/m0/s1
> This means that the [NH3+] is considered chiral, is it expected?
This one is more tricky - InChI wouldn't say this is a stereocenter.
InChI=1S/C20H23NO3/c1-13-7-8-21(14(2)23-13)12-17-11-20(22)24-19-10-16-6-4-3-5-15(16)9-18(17)19/h3-6,9-10,13-14,17H,7-8,11-12H2,1-2H3/p+1/t13-,14+,17?/m1/s1
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