Sounds like a lot of work, getting from Germany to Brazil. North America or the Caribbean are far more plausible.
Not to mention they better be best friends with the English, or they get 100% blocked from their colony every time a war starts. Not to mention the French and the Spanish.
Another problem is that Brazil is a tropical country, and Germans are used to cold climate and a weak, feeble sun of the northern regions. They're gonna fry like lobsters unless they get some race-mixing going with the natives. Their plant cultures are also too wildly different, and unlike the Portuguese they lack the contact with tropical regions to easily bring tropical cultures to Brazil - Brazil is full of cultures from other tropical parts of the world.
Also, Germany has no naval tradition, whereas the Portuguese Tradition IS Naval Tradition.
A HRE colonial effort from Italy is far more likely, but it would be pretty much a Italian Colonization. Also, vulnerable to Spain or Portugal just blocking the Gibraltar Strait and saying "No U" with their mega-fleets.
Naval tradition? Consider the Hansa and North Germany. Old Saxony of the 11th and 12th century could develop a solid naval tradition, just as the Dutch did centuries later. It's possible that Didrik Pining and Hans Pothorst--German privateers--were among those who found their way to the New World before Columbus.
The Germans could try at the Brazilian Northeast (the historic center of wealth), but the other parts of Brazil like Sao Paulo and Minas Gerais might be more profitable in the long run. Especially the Brazilian South with its highland climate, although that would be more linked to the La Plata Region. South Brazil is good for production of sugar, tobacco, yerba mate, and other useful goods.
Race-mixing is inevitable. There will be more men than women, and the locals will be forced to provide their women (this will be a source of conflict, and one which it's likely the Europeans will win). And before long, African slaves--they will farm sugar and other crops--will have their women "taken" by the ruling class. The interior will provide a lot of slaves, and we may have German
bandeirantes active in the area.
No. Portuguese colonization of Brazil was inevitable after they established their Asian empire. The sea routes to India just took European ships way too close to the Brazilian shore.
Any POD which results in a German power which can colonise to begin with would be well before Portugal started their expeditions. And while it's definitely more likely for a German power to focus on the Caribbean (sugar islands) or North America (fur trade, gold in Georgia) due to geography, Germans in Brazil aren't totally impossible either.
Germany had a large population which often settled in Eastern Europe. If Eastern Europe is less amenable to Germans, or incentives to settle the New World are greater, then a lot Germans will likely head for the New World.
I like the idea of a German colony in the Platine region, which has ample opportunities for farming plus trade. It has a good climate like New England or the Mid-Atlantic, so if you send whole families over you'll have a natural rate of increase for your colonists. If they can deal with the local American Indians, then they'll be well off. I think the best way to get Germans to colonise Brazil would be if the motherland develops a taste for yerba mate. Like tea or coffee, it's caffeinated, and IMO it's far tastier than any tea or coffee, and it just so happens that Southern Brazil is a key area for yerba mate plantations. The climate in the highlands of that region are likewise good for European settlement, and also good for planting mate.