Most of the jewish immigrants that came to Brazil from in the begining of the 20th centrury arrived at the ports of Rio de Janeiro or Santos. If your family came to the Baron Hirsch farming settlements ("Jewish settlement" and "free land" suggest this hypothesis), it means they had to travel to the state of Rio Grande do Sul, in Southern Brazil, where those colonies were located, or they traveled by ship to the nearest port (Porto Alegre). If they spent 2 days on a train to get there, so it is very unlikely that their port of arrival was Porto Alegre since the distances from this port to the colonies are not so big (200 miles +/-).
"Flower Island" in Portuguese is "Ilha das Flores". This was the name of the hostel for immigrants that arrived at the port of Rio de Janeiro between 1877 and 1966. Their website: https://www.miif.org.br/ (only in Portuguese, unfortunately). Nowadays it is a museum. The books with the names of the immigrants who staied there are kept the brazilian National Archives and are online. However, they are not indexed, what means that you have to open the book (PDF format) and search for your family page by page. It's a boring task, but not impossible, that's how I found my grandparents' names there. The books are here: http://sian.an.gov.br/sianex/consulta/pagina_inicial.asp (again, only in Portuguese) You have to create an account (click on "Criar Cadastro" and fill the form). Once you're in, go to the menu Favoritos and chose Hospedaria de Imigrantes -> Hospedaria da Ilha das Flores. There are 71 books, you'll have to search for the book that covers the aproximate date of arrival of your family. However, there was no train station there (it's an Island) and I doubt that there was a railway connecting Rio de Janeiro to the Baron Hirsch colonies or nearby cities.
The ship manifests with the names of the immigrants arriving at the port of Rio de Janeiro are also on this website, but with the same problem: you have to open one by one. If you don't know the ship's name or an aproximate date of arrival it's like looking for a needle in a haystack. To open them go to the menu Favoritos -> Relacao Vapores Entrada Porto Rio de Janeiro.
I don't know any place called "Lubinengo". I googled it and found nothing. "Ameriga" sound like "America", but there are many places with America in the name.
"Rainy season in Brazil" depends on the region. In Rio it is between December and March, but it can rain on every month, there is not a dry season. In Rio Grande do Sul it rains a lot between June and September, but, again, it can rain all the other months.
You said your great uncle's baby sister was buried on the region. There are 2 jewish cemeteries close to the Baron Hirsch colonies, in the cities of Passo Fundo and Erechim. Both are in the JewishGen Online Worldwide Burial Registry. Have you tried searching for you family name there?
Hope it helps!