For example, are Brahmin males required to maintain a Shikha, be freshly bathed and bare-chested while performing rituals or wear dhotis in a certain way?
For performing rituals in general the upper garment and the sacred cord should be held in a way that it is over the left shoulder and goes below the right armpit (it's like a loop).
For doing rituals for the ancestors this will be reversed i.e it will be on the right shoulder and under the left arm.
He should wear an upper garment during these five activities: private vedic recitation, voiding urine and excrement, giving a gift, eating, and sipping water
Baudhayana Dharma Sutras 2.6.39
When he is offering sacrifices and softly reciting prayers; When he is paying his respects to elders (A 1.6.32 n.), and when he is eating, sipping water, and doing his private vedic recitation, he should wear his upper garment over his left shoulder and under his right arm
As noted earlier the style will be reversed while performing ancestral rites.
With the formula addressed to ancestors he should make an offering towards the south with his upper garment slung over his right shoulder and under his left arm (A 1.6.18 n.) and his hand turned towards the right.
Apasthambha Dharma Sutras 2.4.6
For the lower garment - the Dhoti - the Parshara Smriti says that it should be worn in the Trikaccha style (where there are 3 tucks/knots).
If, while performing the rite of Achamana, he has his head or throat wrapped with cloth, or the posterior hem of the under-garment is not tucked up, or his coronal lock is not tied, or if he is without his sacred thread, he remains impure, in spite of the ceremony of Achamana.
Parashara Smriti 12.16
So, the undergarment should be properly tucked at the back side as well as the top knot should be in tied condition, while performing rituals.
Similar verses from Baudhayana 188.8.131.52-99:
Three times he should sip water sufficient to reach his heart––without laughing, talking, standing, or looking around; without bowing his head or stooping; never with his topknot untied, his neck wrapped, or his head covered; never hurriedly or without wearing his sacrificial cord over his left shoulder and under his right arm;
Also before participating in a ritual a Brahmin should shave his hairs on the head (saving the top-knot) and on the face:
When he is about to engage in the soft recitation of prayers, make burnt offerings and oblations, and practise restraints, a Brahmin should first get his head and beard shaved and his nails clipped on an auspicious day and under an auspicious lunar mansion during the fortnight of the waxing moon.
Baudhayana Dharma Sutras 184.108.40.206
Any act/rite a Brahmin does with the Shikha (top knot) untied is equal to an act not done. So, the Shikha should always be tied while in rituals. And to be able to tie he should always sport one. One cuts his Shikha when one takes Sannyasa.
A twice-born one should always wear the sacred thread and tie up the tuft of hair on his crown.
He should put on a most excellent white piece of cotton or silk cloth without any hole, but quite different from* the one used before.
Usana Smriti 1.7
One must always put on the sacred thread and bind the tuft of hair on the crown : what one does without having the sacred thread on or without binding the tuft of hair on the crown, is equal to an act not done.
Katyayana Smriti 1.4
While the verses I have given above already show that one must not cut the Shikha because without having it one can not tie it.
But while searching for specific references, I found the following passage quoted in Yajnavalkya Smriti (with three commentaries; easily available on Archive.org):
In the Prayoga Ratna of the author of Nirnaya Sindhu :—" The tuft should be in the middle of the head, but of the Vasisthas towards right, and of Atri and Kasyapa clans, on both sides." So also in the Madhaviya. But Apastamba says : — "He combs the hair silently, and arranges the locks in the fashion of his ancestral Risis." (Ap. G. S. YI. 1ft. 6). According to the number of Pravara and Risi at the time of initiation all these locks except the middle one are cut, from all different directions. " He shaves his hair with the different Mantras, towards the different (four) directions." (Ap. IV. 10. 6.) The middle lock (called Sikha par excellence) should however be never cut for Sruti prohibits it, and so also the Smriti :—" He is as if naked and uncovered who is totally shaven, this Sikha is his covering." *' A person without sikha and without sacred thread cannot perform any sacred rite, for all that he does is unfructuous."
at what age a Brahmin boy should start wearing shikha
After the Chudakarana or tonsure ceremony this style has to be maintained by a Brahmin. The exact age varies with the tradition but it has to be before the 7th year.