The Sankhya-Yoga-Vedanta synthesis of Vijnana Bhikshu

Brahman

Brahman is same as Īṡvara, Paramēṡvara and Paramātman. They are not distinguished like in Ṡāṅkara’s theory.
Brahman is nirviṡēṣa or nirguṇa, i.e., without qualities or without adjectives.
Brahman is pure knowledge (jn̄āna-rūpa). Brahman does not have knowledge as an attribute, but Brahman is the knower, the known and the knowledge itself.
Brahman is self-illuminated.
Brahman is not any god like Viṣṇu or Kṛṣṇa or Nārāyaṇa. They may be considered as partial avatars but not as Brahman.
Jīva is an aṃṡa (part) of Brahman, the whole (aṃṡin); it is not an adjective or qualified item like Rāmānuja says.
Jīva and Prakṛti are the ṡaktis (potencies) of Brahman. That is, Brahman is ṡaktimān, the possessor of ṡaktis. Just like energy cannot be split from the energetic, jīva-prakṛti are considered abhinna (identical).
Jīvas are innumerable but yet they are advaita with Brahman because they are qualitatively the same (sādharmya sharing same behaviours and sajātīyatva in same category of conscious beings)
Prakṛti and its evolutes too are in indivisible state (avibhakta) due to the Satkāryavāda theory of causation (“effect is pre-existent in the cause”). This unmanifested and undivided mūla-prakṛti is nothing but a ṡakti (potency) of Brahman and hence non-different from it.
Brahman is not of the nature of ānanda. That is, Brahman is sat-cit but not ānanda.
There is no world/planet (like Kailāsa or Vaikuṇṭha) that is beyond space and time and full of bliss.
Brahman is the nimitta-kāraṇa (efficient cause) and upādāna-kāraṇa (material cause) and yet non-different from it.
Brahman is with upādhis (adjuncts) during the phases of manifested creation, but not post-dissolution. This upādhi is different from Brahman’s ṡaktis! It is eternal.

Jīva

Jīva is a ṡakti (potency) or an aṃṡa (part) of Brahman. In the sense of a spark being a homogenous part of burning fire - they are qaulitatively same. Not in the sense of jīva being dependent on Brahman (cf. Rāmānuja, Madhva) or jīva being an upādhi of Brahman (Bhāskara).
Jīva is dependent on Brahmaṇ but that is not the meaning of aṃṡa.
Jīva is not aṇu (atomic) but vibhu (all-pervading), though there are infinite jīvas. They don’t form a “lump” of consciousness or anything like that.
The agency (kartṛtva) and experiencing (bhōktṛtva) of jīva are due to upādhis. They are not natural (svābhāvika) and subservient to Brahman (adhīna) like Ramanuja, etc. say.
Jīva and Brahman will never ‘merge’ to form a single union, even after mokṣa. Jīva is never as great as Brahman.
A liberated jīva does not end up in four-handed forms like in Vaikuṇṭha (sāyujya-mukti) or a servant-hood (dāsya) in Kailāsa etc.
Jīva is neither an appearance (fallacious or real) nor a reflection of Brahman. Jīva is not some limited representative of unlimited Brahman. Jīva is not some eternal servant of Brahman either.
Jīva is just that – he is a homogenous part (sajātīya aṃṡa) of Brahman, he is pervasive (vibhu) and is knowledge (jn̄a) too.

Prakṛti

It is accepted that Prakṛti is inanimate and of the nature of three guṇas (sattva, rajas, tamas).
Prakṛti is not independent like in Sāṅkhya but it is an internal potency (antarlīna ṡakti) of Paramātman; just like jīva is also a ṡakti of Paramātman. It is not a form of Brahman (brahma-rūpa).
Prakṛti is not same as avidyā or māyā or akṣara. Prakṛti cannot be considered akṣara because it is ever-changing (pariṇāminī). Each term has its own nonsynonymous meaning.
Just like Mūla-kāraṇa Prakṛti is a form of Prakṛti that is an upādhi of jīva, Māyā is the name of that form of Prakṛti which is an upādhi of Īṡvara.
Māya is not unreal (asat) but actually existing (sat). Māyā is jaḍa (inanimate) but of ṡuddha-sattva and hence of ever-blissful nature (nityānanda) due to the absence of Rajas-Tamas. Hence it is homogenous (sādharmya) with Prakṛti.
Avidyā is a shorthand for five afflictions (pan̄ca-klēṡa) of buddhi, like egoism, passion, hatred, attachment, etc.
The main difference between Mūla-prakṛti and Māyā is that the former is subject to change/transformation (pariṇāminī) but the latter is not.
Prakṛti is real (sat) though transcendental, in the sense that it is a potency of Īṡvara and hence advaita is maintained.
Thus Prakṛti is of these three forms (mūla-prakṛti, māyā, avidyā).

Other entities like time (kāla), prāṇa, adṛṣta, etc. are also considered inanimate ṡaktis of Paramātman but different from Prakṛti anyway.

References:

Acharya Vijn̄ana Bhikṣu and His Place in Indian Philosophy – in Hindi, by Prof. Suresh Chandra Srivastava.