Generally no, but it is possible to stain garments with the spray-on stuff if you don’t use it correctly.
Differently to Flight above, I only use an iron on the absolute minimum heat setting to achieve steam, both for trousers and shirts. Steam the hell out of it, then turn the steam off to go over just enough to dry the garment out again.
I suspect that too much dry ironing is what is causing your shiny patches.
Throw them under a flat cloth with the rank facing down, iron dry for a short stints at a time (they don’t do well with extreme heat or moisture)
Not ideal. Will suit you fine for general wear, but if you’re looking to get an impressive finish then issued DMS will serve you better.
Pretty good so far.