Para is the space-like heart. If there were intellectual analogs then we would not need her reality. She is termed emptiness or void of specific quality, quantity, very much like the Buddhist's emptiness. Her knowledge is nirvana, very much like the Buddhists' nirvana.

Para is freedom. She is not "like" Paramashiva. She is Paramashiva. All Para deities are the same. If they have any character then they are not Para, but some other thing. Para is spacious, and has no direction, no manifest quality, and as heart of Lalita is Shodashi Herself. But can also be called Mahakali Herself. Try not to lock your intellect into a specific formulation and you will come closer to the liberation that is Para.

SuperPollito

Yes, Parā is a deity worshiped within Śrīvidyā, specifically within traditions that follow the Paraśurāmakalpasūtra where she is described in the eighth khaṇḍa entitled, Parā Krama. In this chapter, Parā is spoken of as the 'heart of Lalitā' and is described as white as a spotless moon, having three eyes, two hands (holding a book and the cinmudrā), and is the supreme kalā. The chapter continues with her worship (krama) and how to perform it, but in terms of a deeper understanding of who she is and how the annutarapaddhati of Parā relates to the worship of Lalitā and other deities such as Vārāhī, it is beyond the scope of a post here.

One issue that confuses many people, both established practitioners and lay devotees, is that the definition of the word parā/para simply means supreme and hence it is also a title used to describe various deities who are considered to be supreme. This is why some people may think Parā has no manifest qualities. In fact, several Kaula lineages, including Śrīvidyā, Trika Śaivism, and the Paścimāmnāya, all speak of Parā as a supreme level goddess who has several iconographic depictions, and mūlamantras, that describe her as a goddess as white as the full moon, but also red like the morning sun. She is also described with a number of arms ranging from two to four. Such knowledge of Parā, as a goddess, can be found throughout a large corpus of mūlaśāstra and commentaries by learned gurus. In this sense, Parā has two main forms: 1) she is a solitary goddess, as found within Śrīvidyā, and 2) a goddess who is accompanied by two of her emanations, known as Parāparā and Aparā, as found in Trika Śaivism (Kashmir Shaivism).

Aside from her mantric form and specific deity lakṣaṇa, parā is also state of awareness and a critical part of the famous four levels of language (parā, paśyantī, madhyamā, vaikharī). The key here is that parā is not only some transcendent, higher, supreme level that is pure nonduality untouched by anything and unmanifest, actually just the opposite! Parā is the ground in which the other three levels are based. In this sense, parā is only fully manifested in vaikharī. It is easy to forgot that Paramaśiva is fully in all of the thirty-six tattvas, all the way to the solidity of pṛthvītattva! Paramaśiva is the embodiment of full immanence and full transcendence. In this regard, it is important to study the difference between anaśritaśiva (36th tattva) and paramaśiva (37th tattva).
Driving this point home, the foundational South Indian Śrīvidyācārya, Śrī Śivānandamuni describes parā, as a state of awareness and level of language, with the imagery of a flower:

पराभूजन्मपश्यन्तीवल्लीगुच्छसमुद्भवा ।
मध्यमासौरभा वैखर्यक्षमाला जयत्यसौ ॥ १ ॥
"The garland of syllables (from 'A' to 'KṢA') as embodied speech (vaikharī) is supreme and whose sweet fragrance of intermediate speech (madhyamā) is produced from the blossoming flowers of visionary speech (paśyantī) growing from the solitary ground of Parā. 

I hope this helps. Once you gain more fluency with Śrīvidyā and progress through various levels of sādhana, you will undoubtedly be taught the Parā Krama of PKS and learn, and experience!, more about Parā for yourself, including her mūlamantra and method of worship. Śrīgurubhyo namaḥ!