Bharat,
Pradosha occurs when trayodashi ( the thirteenth day after full moon / amavasya) falls in the evening.
That conjuction (trayodashi + evening) is said to be sacred to Lord Shiva. It is also beleived that he performs his Ananda Tandava during Pradosha.
In fact, there is also a belief that Lord Shiva is so engrossed in his dance that there is no point in asking HIm for favour. So it is a common practice for the devotees to whisper their requests in Nand's ear, in the hopes that he will convey it to the Lord when He is free.
Regarding Vrats, I have no idea, since these practices vary from region to region.
Mahadev is known as Ashutosh - one who is easy to please- because He is happy with something as simple as an abhishekha of water / milk.
See, it is said that each of the five prominent dieties in Hinduism ( Sun, Shiva, Vishnu, Devi, Ganesha) are said to be pleased with one particular act.
For instance - Sun is propiated by offering water / full length namaskar.
Shiva is pleased by an abhishekha. That's why there is a pot of water, with drops dripping, above every Shivalinga.
Vishnu (Rama/ Krishna) is pleased by recitation (Paaraayan) That's why it is considered auspicious to read / hear Ramayan and Srimad Bhagavatam.
Devi ( Durga / Saraswati / Gowri) is pleased when one recties her praises in the form of Shlokas. That's why she is called Stotrapriya Stutimati Shruti samstutha Vaibhava
Ganesha is pleased with... no surprises... Food... Bhojanam.
Now what happens if a person cannot perform Surya namakar, cannnot read Ramayan nor knows any slokas nor is able to cook bhojan?
All he had to do is offer water to a shiva linga and chant Om Namah shivaya and Shiva's grace will be upon him.