Among other things, I understand that a widow is not allowed to give her son/daughter away in marriage, only a husband-wife couple can do so.
Yes, scripture suggests that widows are inauspicious and should be avoided "like the poison of a snake." Only exception is one's own widowed mother.
Julie Leslie, in The Perfect Wife — a translation of/commentary on Strīdharmapaddhati (Guide to the Religious Status and Duties of Women) by Tryambaka of 18th century Thanjavur — says the following.
Tryambaka also discusses the interesting question of the impurity and inauspiciousness traditionally ascribed to widows. The examples he quotes are typical. 'Just as the body, bereft of life, in that moment becomes impure, so the woman bereft of her husband is always impure, even if she has bathed properly. Of all inauspicious things, the widow is the most inauspicious; there can never be any success after seeing a widow (cf. section IIA, pp. 54—7). The wise man should avoid even her blessing (tadāśiṣam api—excepting only that of his mother—for it is devoid of all auspiciousness, like the poison of a snake (āśīviṣopamām).'
According to Tryambaka, however, such remarks apply only to the widow who does not behave as she ought (ācārahīnāviṣayam). For even if she becomes a widow, the pativratā — 'who is devoted to (good) conduct' (caryāparā), 'fully committed to her religious duty' (dharmasamayukta), and 'who follows (the proper path of) widowhood' (vaidhavyam palayet) — earns a threefold reward: she is both happy and auspicious (śubhā) in this life; she obtains the pleasures of heaven (svargabhogān), or indeed the same heaven as her husband (patilokam); and she marries that same husband again in her next life. Theoretically at least, if she behaves as she should (see above), the dread inauspiciousness with which the scriptures threaten her are cancelled out. But if she cannot do this, she would presumably be well-advised to die with her husband.
The answer is No. Vyasa says there are not inauspicious. In fact, a sensible man should worship her.
Kashi Khanda of Skanda Purana chapter 4 contains characteristics of a chaste woman. These are said by Brihaspati. These are again narrated by Vyasa.
After talking about duties and characteristics of a chaste woman, Vyasa continues to talk about duties of a widow.
If a widow does austerities and charity as prescribed for the better lokas of her husband, she is auspicious.
When a widow has love and respect towards her husband, she is auspicious.
It is to be noted that a widow is prescribed to do charity and vratas where Brahmins and sages should be fed. So, one can go and visit her if she is inviting as a part of vratas.
Regarding visit to temples, she is recommended to visit famous temples like Badarikashrama (Badrinath) and offer worship there.
A widow who is fond of her husband, should not do anything without asking her sons. A widow who is accustomed to observe all these vows and practices1 is considered auspicious.
A widow who is chaste and who observes all these pious practices, shall attain the regions of her husband. She shall not be miserable anywhere.
If a woman considers her husband as a deity, there is no difference between her and Ganga. She is directly equal to Umã, the consort of Siva. Hence a sensible man should worship her.
It is clear from the words of Vyasa and Brihaspati that a widow who are fond of their husband and perform charity and worship for the betterment of her husband is equal to Umā, consort of Shiva. She should be worshipped and treated like before.
Skanda Purana says so.
Skanda Purana, Vaishnava Khanda (Book II), Vasudeva Mahatmya (Section IX), Chapter 22:
Of all inauspicious things, a widow is the most inauspicious one. Her sight or touch destroys the merit of men. (11)
If at time of starting on a journey one sees a widow in front, one shouldn't go at that time. Otherwise death is certain. (12)
The blessings of widowed women are similar to the hissing of black serpents. A householder should be afraid of them as of ogresses. (13)