(1) I think STAR deals quite well with the mapping of reads from spliced junctions (I'm not saying that SUBREAD doesn't) and it is quite fast. (I'm not very well familiar with any of these softwares, sometimes is just a matter of taste).
(2) Yes, at least
DESeq2, will require raw (not transformed/normalized) read counts. The normalization will be applied internally by each one of the softewares. For DE analysis you shouldn't use TPM. It is preferable to use raw counts. TPM does not normalize across samples, only within sample, so its not the preferable normalization method in both softwares packages. Also read this: bioconductor.org/packages/release/bioc/vignettes/DESeq2/inst/doc/DESeq2.html#why-un-normalized-counts
(3) Yes, at least
Salmon gives you TPM values. You can use
tximport R package to import these counts to R and directly to
DESeq2. In this case
tximport will try to revert and estimate the raw counts based on
countsFromAbundance method parameter given, and also can summarize reads at gene-level. No. You should always prefer to use raw counts, unless a particular software specifically requires TPM values, for some reason. You can use
featureCounts and then convert this to TPM. There isn't any difference, regardless the difference related to the methods itself (I mean if you use
featureCounts and check the TPMs obtained with both, they can be different, but this difference is due to the mapping/summarisation methods).
I hope this helps,