Are there any Women Rishikas in Vedas ? And are there any rules and proofs Grihya Sutras and other scriptures that women can wear thread?
Prof Mookerji in his "Ancient Indian Education (Brahmanical and Buddhist)" Page 51 says
Women were then admitted to full religions rites and consequently to complete educational facilities. The wife was a regular participator in the sacrificial offerings of the husband [Rv. i, 122,2; 131,3; iii, 53, 4-6; v, 43,15; viii, 31,5; x, 86,10; etc.]. Women-sages were called Rishikds and Brahma- vddinis. The Rigveda knows of the following Rishikas, viz. (x) Romaga [i, 126, 7], (2) Lopamudra pi, 179, 1-6], (3) Apala [viii, 91,1-7], (4) Kadru [ii, 6,8], (5) ViSvavara [v, 28, 3], and several others mentioned in the tenth Mapdala, such as: (6) Ghosha, (7) Juhii, (8) Vagambhpni, (9} Paulomi, (10) Jarita, (11)Saddha-kamayanl, (12) Urvail, (13) Sarnga, (14) Yami, (15} Indrani, (18) Savitri, (19) Devajami, while the Samaveda adds the following, viz. (20) Nodha [Purvarchchika, xiii, 1], (21) Akrishtabhasha, (22) Sikatanivavari [Uttararchchika, i, 4], and (23) Gaupayana [ib., xxii, 4]. The Brahmavadinis were the products of the educational discipline of brahmacharya for which women also were eligible. Rigveda v.7.9 refers to young maidens completing their education as brahmacharinis and then gaining husbands in whom they are merged like rivers in oceans. Rv. iii.55.16 mentions unmarried learned and young daughters who should be married to learned bridegrooms. Yajurveda [viii, i] similarly states that a daughter, who has completed her brahmacharya, should be married to one who is learned like her. The Atharvaveda [xi,6] also refers to maidens qualifying by their brahmacharya, the disciplined life of studentship, for married life in the second airama (brahmacharyeya kanyd yuvanrth vindatepatim).
Regarding Women eligibility to Upanayana and performing sacrifices, PV Kane in History of Dharma Sastras Vol 2 Part 1 Page 151-152 says
The Hārita Dharma Sūtra as quoted in the Sm.C. and other digests says:−'there are two sorts of women, those that are brahma-vadinīs (i.e. students of sacred lore) and those that are sadyovadhūs (i.e. who straightway marry). Out of these brahma-vadinīs have to go through upanayana, keeping fire, Vedic study and begging in one's house (i.e. under the parental roof), but in the case of sadyovadhus when their marriage is drawing near, the mere ceremony of upanayana should somehow be performed and then their marriage should be celebrated.'
In the Gobhila Gr. II.1.19 it is said:− "leading forward towards the sacred fire (from the house) the bride who is wrapped in a robe and wears the sacred thread (slung from her left shoulder, in the yajñopavīta mode) he (the husband) should murmur the verse;− ' Soma gave her to Gandharva ' (Rig. X.85.41)".
It is clear that the girl, according to Gobhila, wore the yajñopavīta as a symbol of the rite of upanayana. Harīta prescribes that in the case of women samāvartana took place before the appearance of menses. Therefore brahmavadinī women had upanayana performed in the 8th year from conception, then they studied Vedic lore and finished student-hood at the age of puberty.
Yama says:− 'In former ages, tying of the girdle of muñja (i.e. upanayana) was desired in the case of maidens, they were taught the Vedas and made to recite the Savitrī (the sacred Gāyatrī verse), either their father, uncle or brother taught them and not a stranger and begging was prescribed for a maiden in the house itself and she was not to wear deer-skin or bark garment and was not to have matted hair '.
There is a great deal of misinformation going around about 20-27 female authors of the Vedas being "rishikas" / human women. Let's get this clear over 99% of the Vedas are authored by males. The female authors passing off as women are also not human. For example:
Indrani = Goddess
Indramata = Mother of Indra
Dakshayani = Goddess
Surya Savitri = Goddess
Yami = Goddess
Yamī Vaivasvatī = Goddess
Aditi = Goddess
Urvashi = Apsara
Sarama = Celestial Bitch
Sarama Devasuni = Celestial Bitch
Sarparajni = Divinity
Dakshina, Vak and Shraddha = Abstractions, symbolism and ritual entities (according to some traditions Vak was possessed by the supreme goddess herself)
Juhu Brahmajaya = Ritual entity (Juhu is the sacrificial spoon), symbolism and abstraction. The hymn deals with the restitution of the wife of a Brahmin, just as King Soma once returned the wife of a Brahmin, apparently Bṛhaspati's wife (verse 5). Gods, men, chieftains should return the wife of the Brahmin, otherwise even "highest heaven" would turn to disorder (verse 4). A woman's voice is not heard here at all.
Godha = Female monitor lizard. There is no voice of any human woman here in Rig Veda 10.134.6b-7.
Ratri = Goddess
Sasvati Agnirasi = Interlocutor in the last stanza of Rig Veda 8.1.34, not author. The authorship of 8.1.34 is ascribed to other people.
Lopamudra = Interlocutor who was created from animal parts. In sexual/Rati hymn.
Gosha: She is probably quoted in 7 verses as the 10.40. 1-5 & 13-14 are both someone else. Even if she is not quoted she is just praying for a husband. Does not seem to be a "Rishika" and is identified as daughter of a king (rajya duhita)
Apala Atreyi = Verse is a quotation. Rig Veda 8.91 itself states that.
So out of 20 authors I have covered maximum 5 human women are actually authoring Vedic mantra and these also are related to sex or relationships. Why? Because in most of the cases women are not supposed to learn Vedas or take Sanyasa. This is clearly given in Sanyasa upanishads and dharmashastras. It is also given in many places in puraans where it is said that a woman's highest duty is to attend to the husband.
Sanyas is possible (as in the case of Shabari from Ramayana), but not recommended at all nor the general trend. It is also debated whether the woman can be a guru or not. So almost forget about anything higher than that like authoring Vedas for things other than sexual or relationship related.