Yes. Just use
:noremap j gj
instead of its version with two "n" -s. If you do not want the rendering work to also work in visual mode, you can achieve the desired behavior with two mappings:
:nnoremap j gj :onoremap j gj
Modeling the behavior of d d is quite complicated, and I could not do it. This command means "delete the current line of the line and put it in the register of the line." The following was my closest attempt, but this requires much more complex text processing:
:nnoremap dd g^dg$:call setreg(v:register,'','al')<BR>
(again, this does not work , but may indicate a useful direction).
You may also be interested in the relevant help section:
:h map-modes
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