What am I doing wrong please?

Slashes are unfortunately not "smart" and do not stay on the same line when transposing - they are just ordinary notes that have been adjusted to look like slash marks (and to not play back). So you do indeed have to transpose them back. I am hoping to see some sort of native slash support in a future version.

As for chord symbols, they transpose if they are recognized by the program but not otherwise. You can control which symbols MuseScore recognizes using the chord description files you select via general style->chord name. Have you read the section pn chord symbols in the Handbook? It explains the various different options. The defaults used in the jazz lead sheet template expect the abbreviations used in the brandt/roemer standard - "ma" for major and "mi" for minor. But I believe the "stdchords.xml" uses the maj/m convention (even though I apparently left that put of the handbook), so switching to that then re-parsing your chords (just double click the first and hold space or tab until it goes through the score) should cause your chords to be recognized. You may need to adjust the font characterisitics (text style->chord name) first to get the look you want.