Which Form of God is referred to as 'Hari' in our scriptures? Does 'Hari' mean the Formless Brahman also?
As the Vishnu Sahasranamam states, Hari is regarded as a name of Sri Vishnu:
kālaneminihā vīraḥ śauriḥ śūrajaneśvaraḥ | trilōkātmā trilōkeśaḥ keśavaḥ keśihā hariḥ
|| 69 ||
The word "Hari" literally means "One who destroys Samsara."
We know from Sri Krishna in the Bhagavad-Gita itself that He indeed is the one who liberates jivas from Samsara:
ye tu sarvāṇi karmāṇi mayi sannyasya mat-paraḥ ananyenaiva yogena māṁ dhyāyanta upāsate teṣhām ahaṁ samuddhartā mṛityu-saṁsāra-sāgarāt bhavāmi na chirāt pārtha mayy āveśhita-chetasām
English Translation: But those who dedicate all their actions to Me, regarding Me as the Supreme goal, worshiping Me and meditating on Me with exclusive devotion, O Parth, I swiftly deliver them from the ocean of birth and death, for their consciousness is united with Me. (Bhagavad-Gita 12.6-7)
Interestingly, Hari is also regarded the name of Mahadeva according to the Shiva Sahasranamam:
nimittastho nimittam cha nandirnandikaro harih nandiishvarashcha nandii cha nandano nandivardhanah || 46 ||
However, "Hari" is more popularly used to refer to Sri Vishnu.
The term "Hari" is also used to refer to an incarnation of Vishnu:
tatrāpi jajñe bhagavān hariṇyāṁ harimedhasaḥ harir ity āhṛto yena gajendro mocito grahāt
In that Manvantara the Lord too was born through Hariṇī from (the loins of) the sage Harimedhā (her husband) and was named Sri Hari, by whom Gajendra, the (celebrated) leader of (a herd) of elephants was extricated from (the grip of) an alligator. (Srimad Bhagavatam 8.1.30)
The form of God referred to as 'Hari' is Sri Vishnu, Sri Krishna or His different incarnations.
Lord Shiva is also referred to as 'Hari' in the Shiva-Shasranama, but our scriptures do not use the word 'Hari' to imply Lord Shiva. Otherwise, we would not have a separate dhyana-sloka for 'Hari-Hara'. An image of Hari-Hara is enclosed. The dhyana-sloka of Hari-Hara is
shulam chakram pAnchajanyam abi_iti dadhatam karaih/sva-sva-bhushat sva-lilArdha-deham hariharam bhaje//
In the svarupa, both are the same and some names commonly known as of Lord Shiva like 'Swayambhu', 'Sambhu' etc are included in the Vishnu-sahasranama also.
But all our scriptures unianimously mean Lord Vishnu or Lord Krushna by Hari.
So there is no room of confusion here.
Srimad-Bhagavatam however repeatedly speaks of both the aspects of Sri Hari ---with form and without form. For example, Sri Hari Himself describes His formless svarupa as
The Supreme Brahman, who is extremely subtle, being of the nature of pure Existence-Consciousness-Bliss, unlimited and impossible to be conceived with an impure heart (10.88.10).
So yes, 'Hari' means the formless Brahman also.