Are the Fastq files content is truly random
In my experience, the distribution of reads on the flow-cell is pretty much random, but the sequencing errors are not necessarily randomly distributed.  In all Illumina instruments I have seen, it is common to see edge-effects, or other localities on the flow cell where the error profile differs from the rest of the cell, and QC pipelines generally test for this problem.

A particular issue with the HiSeq3000/4000 patterned flow-cells is that, in situations of under-clustered runs, it would be typical to find the same sequence repeated multiple times in nearby 'clusters' - in other words, a clustering of clusters all containing replicates of the same underlying molecule.  Even for runs where there is no severe under-clustering, it might be expected that duplicates would be found in adjacent cells.  qcfail.com has an outline of this phenomenon: https://sequencing.qcfail.com/technologies/hiseq/