Basic floor area ratio / floor area ratio for plots without a development plan: How to calculate? Experiences?

Where is the difference here?

The urban planners are responsible for planning law issues, so exactly your topic. Is it possible to build here according to §34? Is there a type of area according to the Land Use Ordinance? How large is the degree of structural use (site coverage ratio/floor area ratio, number of floors)? Are there factual building boundaries? The building supervision is responsible for compliance with the state building code. Keywords: clearance areas, fire protection, escape routes, noise protection, playgrounds, parking spaces, development, ..., i.e. the details to be clarified in the second step.

in fact, the neighboring plots are already partly developed.

What exactly has been built on the neighboring plots? Are there already multi-family houses? How large are the plots? Are the houses detached? How many floors do they have?

but in my opinion, a fluctuation of the floor area ratio between 0.8 and 1.5 is far too large for a calculation

According to your information on the standard land value, an average floor area ratio of 1.0 applies in this area. If your neighbors do not deviate significantly from this, you can assume a range of 0.9 to 1.1 for your plot.

what determines whether a project is realized according to §34 Baugesetzbuch or a project-related development plan is drawn up.

You need a development plan (or the municipality does), if the requirements of §34 Baugesetzbuch are not met, i.e. if the plot is located outside the built-up area of the locality, e.g. on the outskirts, or if the urban planners do not want to supplement the existing development with a similar one at the moment, e.g. if they want to allow multi-storey residential buildings in an area predominantly consisting of single-family houses, or vice versa.