Also, what diseases are Papaya plants subject to?
You can plant at any time that the temperature remains above 60 F. These articles will help:
We have a young papaya tree growing in our flower bed one foot from the base of our house in the Southern Nevada area. We are wondering if this can be problematic or cause structural problems to the house. Thanks.
That is too close for any tree. Trees need room to grow and develop a full canopy, plus the roots need to spread. Can you relocate it? This article tells their optimum location.
https://www.gardeningknowhow.com/edible/fruits/papaya/growing-papaya-fruit.htm
https://www.gardeningknowhow.com/ornamental/trees/tgen/transplanting-trees.htm
How to prepare the soil. Do you plant these seeds in a large vessel then transfer when sprouts are established into the soil? What do u suggest.
You don't need a large vessel to start seeds indoors. If you are only planting a few seeds, start with a couple nursery pots that are about a gallon size. Use commercial seed starting mix. These articles should help:
https://www.gardeningknowhow.com/edible/fruits/papaya/growing-papaya-fruit.htm
https://www.gardeningknowhow.com/edible/fruits/fegen/planting-seeds-from-fruit.htm