Why was Sita born from the Earth and not a womb?

It's backstory is in Uttar Kand where it's written that a daughter of Sage Kushadhwaja was very beautiful and many men wanted her hand but he refused them all saying that he wanted Lord Vishnu to be her husband. A demon named Shambhu due to this killed Kushadhwaja and his wife due to grief entered fire. Unprotected Vedvati left for the woods and wore matted locks and black antelope’s skin and did penance to get Lord Vishnu as her husband.

Ravana once saw her and praised her beauty. She introduced herself and called her Vedas personified. He proposed her and called her penance unworthy as she was very beautiful and young. When she rejected his offer, he grabbed her hair which angered her. She cut her hair through her hand which magically became as sharp as blade due to her penance. She entered fire vowing to return and destroy Ravana.

She later was reborn on a lotus with fragrance of lotus. Ravana saw her and brought her in his palace but his ministers seeing her told him that she would be the reason of his destruction. Ravana got angry and threw the baby in the Sea which was taken to Mithila by the waves and when Janaka was doing ritual ploughing ,he found the baby (reborn Vedvati) in the line of ploughed field and therefore named her as Sita and adopted her as his child. He gave her to his Queen and reborn Vedvati became Sita, Princess of Mithila.

Ironically, if Ravana had not thrown the baby despite his ministers warning him, Sita would not be brought up by Janaka but Ravana. But, he was unworthy to become father of Mahalakshmi and therefore she chose Rajrishi Sheerdhwaj Janaka as her father and fate played it's course.

Source- Uttar Kand, Valmiki Ramayana

How is Lord Shiva born?

 Shiva was born from the rage of Narayana!!!

When Brahma's night wore off, through the grace of that Being of immeasurable energy, a lotus made its appearance first, O thou of eyes like lotus petals. Within that lotus was born Brahma, springing from Aniruddha's grace. Towards the evening of Brahma's day, Aniruddha became filled with wrath, and as a consequence of this, there sprang from his forehead a son called Rudra vested with the power of destroying everything (when the hour for destruction comes). These two, viz., Brahma and Rudra, are the foremost of all the deities, having sprung respectively from the Propitiousness and the Wrath (of Aniruddha). Acting according to Aniruddha's direction, these two deities create and destroy. Although capable of granting boons unto all creatures, they are, however, in the matter of the concerns to which they attend (viz., Creation and Destruction), merely instruments in the hands of Aniruddha.

-Mahabharata, Santi Parva, Chapter 342

And again Krishna says

That Being whom, at the time of all thy battles, thou beheldest stalking in thy van, know, O son of Kunti, is no other than Rudra, that god of gods, otherwise called by the name of Kaparddin. He is otherwise known by the name of Kala, and should be known as one that has sprung from my wrath. Those foes whom thou hast slain were all, in the first instance, slain by him.

-Mahabharata, Santi Parva, Chapter 344

Obeisance to Nārāyaṇa, who is pure and eternal. Obeisance to the Lord of all past, present and future, who is in the form of Lord Śiva and auspicious Lord, the origin of Lord Śiva, and the most worshipable of Lord Śiva. Obeisance to Sri Hari, who assumes the most terrible form to end the Kalpa, who is of universal form, Lord of the universe and the supreme soul.

-Mahabharata, Anushasana Parva, Chapter 13

You are the creator. You are the destroyer. You support the worlds. You are Kāla, the destroyer of all. All the clans of Devas were created by you alone, O God. You are the path of all the worlds. You are salvation, the greatest goal. Brahmā, the eternal one of the Rajas form is the Lord born from you. Rudra originating from (your) Krodha (Anger) is also so (born from you). You are established in Sattva. O Lord, the mobile and immobile beings have been created by you for the sake of sport.

-Skanda Purana, Reva Kanda, Chapter 20

May the Lord of unlimited glory be favourably disposed to us—the Lord from Whose strength was born the great Indra, from Whose grace the (various) gods; from Whose wrath sprang up god Śiva, the Lord of mountains; from Whose intellect came forth god Brahmā; from the appertures in Whose bodies were created the Vedas and the sages, and from whose generative organ, the god Prajāpati.

-Srimad Bhagavata Purana, Skanda 8, Chapter 5

So Shiva was born from the wrath of Vishnu.

When was Mother Lakshmi born?

 

According to mythology, Mother Lakshmi was born on the day of Sharad Purnima. Mother Lakshmi originated during the churning of the ocean.

The story related to the birth of Mother Lakshmi:

• Mother Lakshmi was the daughter of Bhrigu Rishi and his wife Khyati.
• Mother Lakshmi's brothers were Dhata and Vidhata and sister was Alakshmi.
• Mother Lakshmi married Lord Vishnu.
• Mother Lakshmi did severe penance on the seashore.
• Devraj Indra took the form of Lord Vishnu and asked Mother Lakshmi to ask for a boon.
• Mother Lakshmi asked Indra to show him the Vishwaroop.
• Indra returned from there feeling ashamed.
• Later Lord Vishnu himself came and asked Mother Lakshmi to ask for a boon.
• Lord Vishnu accepted Mother Lakshmi as his wife as per her wish.

Some more things related to Mother Lakshmi:

• Mother Lakshmi is called the goddess of wealth.
• The vehicles of Goddess Lakshmi are owl and elephant.
• Goddess Lakshmi is considered the goddess of Friday.