Hello @fshapt
Yes, all of this seems possible to do in Galaxy! 
Are you following a published protocol? We don’t have a tutorial for exactly this, so having some outline of the basic steps and an idea of what final outputs you want is a good idea. Galaxy will have the exact or analogous tools, and we can help you to identify them.
For practical first steps, you’ll will want to load up your reads, reference genome, transgene sequence, baseline reference annotation, maybe create a custom annotation record for your transgene, and then optionally prepare a SnpEff reference.
- FAQ: How to use Custom Reference Genomes? (covers both the genome fasta + annotation)
- Quality Control Start Here! multQC issue and guidance? (see the workflow!)
UCSC hosts a version of your reference genome, or you can get the data from NCBI, or you can use what you may already have. Try to prepare all of your baseline reference data at the very start!
- UCSC Genome Browser Downloads (chinese_hamster)
- Index of /goldenPath/criGriChoV2/bigZips
- FAQ: NCBI reference data
If you are completely new to Galaxy, I would strongly suggest taking an hour or so to go through at least one tutorial! Galaxy hosts the common bioinfomatics tools many use for projects like yours, plus utilities for intermediate/custom data parsing, and a robust GUI-based workflow design and execution engine.
Good places to start
- Data manipulation, workflows.
Hands-on: Galaxy Basics for everyone / Galaxy Basics for everyone / Introduction to Galaxy Analyses - QA, mapping
Sequence analysis / Tutorial List - And while this tutorial focuses on variant calling, the early steps are similar across protocols.
Hands-on: Exome sequencing data analysis for diagnosing a genetic disease / Exome sequencing data analysis for diagnosing a genetic disease / Variant Analysis - Then, full assembly is covered here. You might not need it, and I wouldn’t attempt the full genome – just the region of interest + junctions – since the remainder can be derived directly or characterized with variants.
Assembly / Tutorial List
That’s a lot of information! Please review and let us know if you have any questions! 