Learning HIndu - Vishnu

yes, it is one trinity. the creation, support, and destruction of being.

The aim of life is attaining Moksha in Hindu Culture. Although the moksha can only be attained when someone gets free from the desires, bondings and starts to experiences his consciousness one with the supreme consciousness. Moksha is when you are freed from the cycles of life and birth. To achieve this there are four major paths.

Path -> Problem -> Solution
1. Gyan/Janana Yoga(includes Advaita) -> Ignorance -> Knowledge
2. Bhakti Yoga (Devotion) -> Lack of Faith -> Devotion(Love for God)
3. Karma Yoga -> Desires/Attachments -> Selfless Action
4. Raja Yoga(popular as Yoga) -> Restlessness of Mind -> Meditation

Most of the people know Hindu culture as just second path and term Hindu Culture as polytheist, whereas it is actually a pluralist way to attain the aim of life, i.e. moksha.

Lord Krishna is avatar(not specifically incarnation) of Lord Vishnu. While Buddha is not considered as avatar of Lord Vishnu.

As in the trinity of Gods in Hindu culture, the responsibility of maintaining the consciousness in humans and to keep the system of this planet in a workable environment to enable humans to achieve the true consciousness and to reestablish the righteousness, lies with lord Vishnu. So he mostly takes the avatars for few reasons. I am citing two of them from my understanding.

1.
यदा यदा ही धर्मस्य ग्लानिर्भवति भारत।
अभ्युथानमधर्मस्य तदात्मानं सृजाम्यहम्।। Srimad Bhagwat Gita 4.7।।

परित्राणाय साधूनां विनाशाय च दुष्कृताम् ।
धर्मसंस्थापनार्थाय सम्भवामि युगे युगे ॥ Srimad Bhagwat Gita 4.8॥

Whenever there is privation of dharma, then I come.
When iniquity increases, then I manifest as incarnation.

In order to deliver the devout and to eradicate the heretical,
as well as to reestablish the essence of dharma,
I adventured Myself millennium after millennium.

2.
To show and establish their faith humans that, yes there is still a way to life with righteous and successful life even in these circumstances. To show them the right path, who are not enlightened.

Actually this all is very deep and complex, Please feel free to ask if you have any other question.

Brahman is the supreme reality. The Ultimate truth. The one God, if you wish to call that.

The trinity, Brahma, Vishnu and Shiva are Devas or deities. But of higher spiritual elevation. They are not 'the God'.

Krishna and Buddha are NOT the physical incarnations of Vishnu or any of the trinity. They are Guru's, highly elevated enlighten beings who takes birth to establish the Will of the God for a particular era. As the Prophets, Apostles or other spiritual masters have done.

In fact such Masters have reached much higher spiritual heights than the Trinity or Devas or Deities.

But the story tellers, Scholars and poets, who lack the spiritual wisdom attempts to describe these Masters as Avatars of the Trinity.

on a second note - Lakshmi is Vishnu's divine consort or in other words like his feminine half. Parvati and Sarasvati included in the female trinity to go along with Vishnu's.

"an auspicious fortune is attached to their words"

—Rig Veda, x.71.2 —translated by John Muir[64]

Lakshmi features prominently in Puranas of Hinduism. Vishnu Purana, in particular, dedicates many sections to her and also refers to her as Sri.[75] J. A. B. van Buitenen translates passages describing Lakshmi in Vishnu Purana:[75]

Sri, loyal to Vishnu, is the mother of the world. Vishnu is the meaning, Sri is the speech. She is the conduct, he the behavior. Vishnu is knowledge, she the insight. He is dharma, she the virtuous action. She is the earth, the earth's upholder. She is contentment, he the satisfaction. She wishes, he is the desire. Sri is the sky, Vishnu the Self of everything. He is the Sun, she the light of the Sun. He is the ocean, she is the shore.