Exact match with fuzzy query

I am using lucene 3.0.1. I use a MultiFieldQueryParser with
a GermanAnalyzer. In my index are some values among others
one document with the title "bauer". I append to every word
in my query a ~0.8 (here I am not sure if this is the way to
do it). If I try to search now, I will not get the document
with title "bauer" except I set the fuzzy value to very low
values of about .3.
Do i have to perform two searches with and without the
fuzzy parameter or can I do it somehow in one step like
using "bauer~0.8 bauer" as query?
Yes bauer~0.8 bauer as query will bring you both exact and fuzzy matches.
I saw that the parser cuts of the "er" if I am not using
the fuzzy parameter. Can someone please tell my in a few
words why?
This is answer of you question. FuzzyQuery is not analyzed. In your index you have bau, in your query you have bauer. Thats why 0.3 slop is required.
How can I do a fuzzy search which also finds exact matches?

Yes bauer~0.8 bauer as query will bring you both exact and fuzzy matches.

and fuzzy matches.

Is this the normal way to do it?