Can I visit the whole continent in one trip?

You can, but you will spend a massive portion of your budget on flights. It is better to focus on one region per trip.

Is it safe to travel during the rainy season?

It is safe, but expect frequent travel delays due to landslides in the Andes or muddy roads in rural areas.

When to visit South America's diverse climate zones

South America is massive, so aim for the shoulder seasons (April-May or September-October) to avoid the extremes of the Amazon wet season or the Patagonian winter. Choose your timing based on your primary destination: the Andes are best in the dry winter, while the Southern Cone shines during the austral summer.

Define your primary climate zone. Decide if you are chasing the tropical north (Colombia/Amazon), the high-altitude Andes (Peru/Bolivia), or the temperate south (Chile/Argentina). Trying to do all three at once is a logistical nightmare.
Target the Dry Season for the Andes. Visit Peru, Bolivia, and Ecuador between May and September. High-altitude trekking is dangerous or impossible during the heavy rains of December through March.
Avoid the Peak Patagonian Winter. Patagonia is best from November to March. If you go outside this window, many park trails and hotels close completely due to extreme cold and gale-force winds.
Work around the Amazon Rainy Season. The Amazon is humid year-round, but aim for June through November to avoid the peak flooding months, which makes river travel and jungle trekking much harder.

Can I visit the whole continent in one trip?: You can, but you will spend a massive portion of your budget on flights. It is better to focus on one region per trip.
Is it safe to travel during the rainy season?: It is safe, but expect frequent travel delays due to landslides in the Andes or muddy roads in rural areas.