In logUQ scaling, each sample is scaled by the 75th percentile of its count distribution, then the data is log transformed. CSS is similar, except it enables a flexible scaling factor for each sample, that depends on the distribution of counts in each sample. Only the segment of each sample's count distribution that is relatively invariant across samples is scaled. This mitigates the influence of higher abundance OTUs on lower abundance OTUs when the scaling is done.
This scaling does indeed result in non-integers, that are then log transformed. If you use CSS, it would be advised that you double check that after normalization, the samples are not clustering by original (before normalization) library size, by e.g. PCoA or PERMANOVA. This doesn't happen much in weighted unifrac, but for metrics like unweighted unifrac, it may be best to just rarefy, depending on how different your library sizes are.
Hope that helps!