Not if the insert size has an impact on your analysis. Insert size is unrelated to read length for Illumina data. You can calculate the insert size distribution by mapping or merging the pairs (e.g. BBMerge).
Additionally, insert size estimates from lab analysis are often very different from those produced by bioinformatic analysis. For bioinformatics, the latter is necessary.
Yes, but use caution while using it.
Just to be sure, you can take a small subset of the reads, map them to the reference and calculate the insert size. If you use bwa mem, you can even see this in the logs. If the number seems to be close to what is mentioned on NCBI, then go ahead! It should be quick and easy!