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 MP4 ni o dara ju ti o dara ju ti o dara ju: H.264 fidio pẹlu AAC orin orin lori gbogbo foonu, aṣawakiri ati TV laisi package codec, the conversion generally makes gradients look better, not worse.
No — the source has no sound, so the MP4 is silent. Some platforms prefer a video to have an audio track; add a silent or music track afterwards if a specific platform complains.