What you have there is a RNA-seq dataset, the common raw data format would be fastq, not fasta. There is plenty of documentation available on the web that explains what RNA-seq, fasta and fastq is, and what you can do with it. I am not going to write that all down here. For starters you should get familiar with RNA-seq, e.g.
https://www.annualreviews.org/doi/abs/10.1146/annurev-biodatasci-072018-021255
https://www.bioconductor.org/packages/devel/workflows/vignettes/rnaseqGene/inst/doc/rnaseqGene.html
...plus the plenty of materials available online. No, do not remove duplicates. Please google for duplicates + RNA-seq once you understand what the files are, this has been discussed many times before. To make the data "usable" you have to align them to a genome/transcriptome, this is covered in the linked articles.
In short:
1) why duplicates, because the same piece of (c)DNA has been sequenced multiple times, this can either be a true duplicate or a PCR artifact.
2) it is slightly more complicated than "is my gene in there", I think that will clarify after reading the linked articles
3) RNA-seq