There are two different data sources in this case. The data is not the same, though (if you search the same city in the two platforms, the results are different).
INPE is the National Institute for Spatial Research, associated to the brazilian Ministry of Science, Technology, Innovation and Communications.
INMET is the National Institute for Meteorology, associated to the brazilian Ministry of Agriculture, Livestock and Supply.
Both links provide the same kind of information, but due to measurement differences, they are not exactly the same.
None of them offers files to download.
To make informational use, the platform displays data quite easily. But if you want to do anything more complex than that it is not possible because the data is not downloadable.
This year survey doesn't demand information on historical data but only forecasts.
For historical data, it is possible to retrieve information per measurement station, hourly, through the link https://www.inmet.gov.br/sonabra/pg_dspDadosCodigo_sim.php?QTUxMw==
Time series are provided in this link: https://www.inmet.gov.br/portal/index.php?r=estacoes/estacoesConvencionais
There is also a database that requires login and password to access it, but it is for free. You only have to register. It is called BDMEP (Banco de dados meteorológicos para ensino e pesquisa - Meteorological Database for Education and Research). The link is https://www.inmet.gov.br/portal/index.php?r=bdmep/bdmep
The INMEP states that public information can be republished freely. However, it becomes not clear whether weather data is public information or not. Also it becomes not clear whether data can be compiled or modified. Therefore it was answered that the data is not openly licensed. Thank you, Wagner Faria de Oliveira, for contributing to the Global Open Data Index.