Are there any cases when the name of a genus equal to the name of a higher taxon: family, order, class, etc. in botany and zoology?
I answer for botany: no.
The International Code of Nomenclature for algae, fungi, and plants has strict requirements on names:
Article 16.1 has:
The name of a taxon above the rank of family is treated as a noun in the plural and is written with an initial capital letter. (...)
Article 18.1 has:
The name of a family is a plural adjective used as a noun; it is formed from the genitive singular of a name of an included genus by replacing the genitive singular inflection (Latin -ae, -i, -us, -is; transcribed Greek -ou, -os, -es, -as, or -ous, and its equivalent -eos) with the termination -aceae (but see Art. 18.5)
And article 20.1 has instead:
The name of a genus is a noun in the nominative singular, or a word treated as such, and is written with an initial capital letter.
On later article it is explained how to latinize names, with simpler rules (compared to Latin). So genus are singular and higher rank are plural.
Additionally, for botanical nomenclature, an name for ranks between family and phylum rank is made usually by concatenating a genus name with some suffixes (which are rank specific, see article 16.3, 18.1). So reading a name, one could derive also the rank. Just few families still have a old name, but still ending with 'ae' (e.g. Compositae, Cruciferae, etc., Art 18.5). Now (just since 2011-2012 version) there are more exceptions in code, but for historical reasons and for names outside plants in stricter term.
Note: Some old names are automatically corrected with new rules (see e.g. 18.4), so we should have not equal names.
If you take all the taxons into consideration, yes, it can sort of happen - particularly on the genus/species level. The confusion is generally avoided since species are usually referred to by genus and species, using the name twice, whereas the genus is simply referred to by the genus name.
For example, the genus Vulpes includes all true foxes. (Wikapedia)
The genus Vulpes includes multiple species, such as the arctic fox (Vulpes lagopus), the swift fox (Vulpes velox), etc. One of the most widely distributed species of fox, however, is called the Vulpes vulpes, also known as the red fox.
As Remi.b said in his comment, this is very unlikely to happen in higher taxons, since there are general rules that are followed in their naming, and it changes from level to level.
The purpose of nomenclature is to distinguish groups of entities that are worth distinguishing.
Giving the same name to different groups of entities would be absurd. It sometimes happens by mistake, but when such an absurdity is detected by the scientific community, the newly proposed name must be changed to be validly published (and recognized by the scientific community).