Not sure how you performed the search but the Manusmṛti verses cited in the Nirmukta article can be easily found in Ganganath Jha's translation available at Wisdomlib.org. Here's the one-to-one mapping of some of the verses and their translations from both websites:
Nirmukta.com:
Here are some of the ‘celebrated’ derogatory comments about women in the Manusmriti:
1. “Swabhav ev narinam …..” – 2/213. It is the nature of women to seduce men in this world; for that reason the wise are never unguarded in the company of females.
Wisdomlib.org:
svabhāva eṣa nārīṇāṃ narāṇāmiha dūṣaṇam |
ato'rthānna pramādyanti pramadāsu vipaścitaḥ || 213 ||
It is the very nature of women to corrupt men. It is for this reason that the wise are never unguarded regarding women.—(213)
Nirmukta.com:
4. “Naudwahay……………..” – 3/8. One should not marry women who has have reddish hair, redundant parts of the body [such as six fingers], one who is often sick, one without hair or having excessive hair and one who has red eyes.
Wisdomlib.org:
nodvahet kapilāṃ kanyāṃ nādhikāṅgīṃ na rogiṇīm |
nālomikāṃ nātilomāṃ na vācāṭāṃ na piṅgalām || 8 ||
He should not marry a maiden with tawny hair, nor one with superfluous limbs, nor one who has disease, nor one who has either no hair or too much hair, nor one who is garrulous, nor one with reddish eyes.—(8)
Nirmukta.com:
14. “Na ashniyat…………….” – 4/43. A Brahman, true defender of his class, should not have his meals in the company of his wife and even avoid looking at her. Furthermore, he should not look towards her when she is having her meals or when she sneezes/yawns.
Wisdomlib.org:
nāśnīyād bhāryayā sārdhaṃ naināmīkṣeta cāśnatīm |
kṣuvatīṃ jṛmbhamāṇāṃ vā na cāsīnāṃ yathāsukham || 43 ||
He shall not eat with his wife; nor shall he look at her while she is eating, or snoring, or yawning, or sitting at her ease.—(43)
Nirmukta.com:
17. “Balya va………………….” – 5/150. A female child, young woman or old woman is not supposed to work independently even at her place of residence.
Wisdomlib.org:
bālayā vā yuvatyā vā vṛddhayā vā'pi yoṣitā |
na svātantryeṇa kartavyaṃ kiṃ cid kāryaṃ gṛheṣvapi || 145 ||
Whether she be a child, or a young woman, or an aged woman, she should not do any act by herself, even in the house.—(145).
Nirmukta.com:
27. “Pita rakhshati……….” – 9/3. Since women are not capable of living independently, she is to be kept under the custody of her father as child, under her husband as a woman and under her son as widow.
Wisdomlib.org:
pitā rakṣati kaumāre bhartā rakṣati yauvane |
rakṣanti sthavire putrā na strī svātantryamarhati || 3 ||
The father guards her during virginity, the husband guards her in youth, the sons guard her in old age; the woman is never fit for independence.—(iii).
Nirmukta.com:
37. “Ati kramay……………” – 9/77. Any women who disobey orders of her lethargic, alcoholic and diseased husband shall be deserted for three months and be deprived of her ornaments.
Wisdomlib.org:
atikrāmet pramattaṃ yā mattaṃ rogārtameva vā |
sā trīn māsān parityājyā vibhūṣaṇaparicchadā || 78 ||
If the wife disregards her husband who is mad, or intoxicated, or afflicted by disease, she should be deprived of ornaments and appurtenances and abandoned for three months.—(78)
My question is, are there more versions of Manusmriti or are these verses fake?
I don't think these verses are fake because you can find similar ones in other smṛtis as well. E.g., Take a look at Ganganath Jha's notes on Manusmṛti 5.145:
bālayā vā yuvatyā vā vṛddhayā vā'pi yoṣitā |
na svātantryeṇa kartavyaṃ kiṃ cid kāryaṃ gṛheṣvapi || 145 ||
Whether she be a child, or a young woman, or an aged woman, she should not do any act by herself, even in the house.—(145).
Comparative notes by various authors
Gautama (18.1).—‘A wife is not independent with respect to the fulfilment of the sacred law.’
Baudhāyana (2.3.44).—‘Women do not possess independence.’
Vaśiṣṭha (5.1).—‘A woman is not independent; the males are her masters.’
Viṣṇu (25.12).—‘Not to act by herself in any matter (is the duty of the woman).’
As to different versions of Manusmṛti, I'm aware of only two:
The standard version which most people refer to, available at sacred-texts.com (George Bühler's translation) and wisdomlib.org (Ganganath Jha's translation). Any minor differences between various recensions (of the standard version) should be resolved in Patrick Olivelle's critical edition. You can read Author, Date and Title (under Introduction, p. 18) to learn who wrote the Manusmṛti and when.
A Hindi translation by Dr. Surendra Kumar titled "The Vishuddha Manusmriti" (i.e., "pure" Manusmṛti) published by the Arya Samaj which identifies about 1471 verses (from a total of 2685) of the standard version as anti-Vedic interpolations (late additions to the text).