When projecting data with UMAP, should I use only the samples I need projected or the entire dataset?
Yes, more data will improve the quality of the embedding UMAP can produce. While UMAP is somewhat robust/stable under subsampling in general you will get significantly better results with more data. It is also worth noting that most UMAP implementations are not designed for very small datasets (they make some optimization choices that assume a a reasonable dataset size). In practice it is probably best not to use UMAP with less than 100 or so data samples.