They can improve. A palette-limited source is restricted to 256 colours, and video codecs are full-colour, so banding in the source stays but no new banding is introduced. Where WebM ní àwọn ààyè-iṣẹ́ wẹ́ẹ̀bù tí a kò fi ẹ̀yàn-ìdáràn-ìpàdé - vidéòlù VP9 tàbí AV1 láti ní ìrànwọ́ Opus, tí a fi àwọn àmì-ìwé ìṣàfarawé kọ́òdù nípa àwọn ìṣàmúlò-ètò gbogbò tí a tí wa, the conversion generally makes gradients look better, not worse.
No — the source has no sound, so the WebM is silent. Some platforms prefer a video to have an audio track; add a silent or music track afterwards if a specific platform complains.