George Washington was generally skeptical of the role of political parties in a democracy. He believed that having different parties could potentially lead to sectionalism, which could threaten the unity of the nation. He also believed that the conflict that arises between different parties weakens the government, as they try to take the power for themselves and forget about the good of the nation as a whole.
The tiny invaders being discussed in the article are plants. They are considered invaders because they came from other countries, but are now threatening the native plants. People brought them in because they wanted to make their gardens and yards beautiful because the plants are very rarely found locally.