To add to @colinbrislawn's great comments, I'll add one minor detail..
The reason why the "other eukaryotes" are included within the UNITE database is to act as set of outgroup / decoy / off-target taxa. The purpose of these outgroup taxa is to make sure that you properly classify fungi as fungi.
Meaning, if there is nothing but fungi in the reference data set, then most things, even if they are not fungi, will often be misclassified as "k__Fungi", with no further taxonomic level of classification.
So, having these outgroups will increase the chances of properly classifying your features as fungi if they really are, and as non-fungi if they are plant, metazoa, etc... Then you can remove these taxa if they are not part of your research focus. That is, this is no different than removing chloroplasts and mitochondrial sequences from bacterial data sets. Some even remove taxa that do not have at least a phylum level classification.
Also, terms like incertae sedis, is not an actual taxonomy, is is simply Latin for 'of uncertain placement'.
I hope this helps you decide which is the best way to go. 
-Mike