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The cardinal "a half" is unrelated to "two", whereas "a third", "a quarter" (and certainly "a fourth"), etc. are related to "three", "four", etc. This seems to be true in other languages, too, in various language families:
Two questions:
As I suspected, this is indeed a case of suppletion, a term defined by A Glossary of Historical Linguistics as
The use of two or more originally unconnected forms (roots, stems) in the inflection of a single lexical item, for example, go/went, where originally went was not part of the tenses of ‘to go’ but rather was the past tense of wend, which was taken over as the past of ‘to go’ and incorporated into its inflectional paradigm.
Examining your examples:
Portuguese metade is cognate to meio, from Latin medius, ultimately from PIE *medʰyo- (‘between’). Analogously for other Romance languages.
German Hälfte comes from Proto-Germanic *halbaz, which is connected with the Indo-European root *(s)kel- ('to split'). Analogously for other Germanic languages.
Scottish leth comes from Old Irish leth, (‘side’). Analogously for other Goidelic languages.
Hebrew חצי is derived from the root חצה ('to divide').
Hungarian fél comes from Proto-Uralic pälä ('side'). Analogously for other Uralic languages.
Accorging to Fisiak, this is the same process that caused the irregularity one → first, two → second in several languages. Since the word for half (as the words for first, second and third) is much more frequently used than the words for other fractions, it tends to maintain its irregularity over time. Another source of this irregularity is that children do not learn to count as one → first, two → second, etc. Instead, they learn the ordinal and cardinal sequences separately. This is probably what happens to the fraction numbers as well, which constitutes another barrier to regularization.
