For taxes I use the online version of WiSo Steuer for example: https://www.steuer-web.de These services can pull your records on file from the tax office, so all you have to fill in is any additional items (deductible expenses over the year for example).

I don't know any of the details of how the company made the employment work. If you PM me I will give you the name of our German accounting firm which handled everything.