Could anyone please share what their sadhana is like during Brahma muhurta? What rituals and mantras do you chant and in what order? Do you do achamanam and pranayama? Chant mantras or sing bhajans? Meditate?
What Sadhana one should perform at Brahma-Muhurta is described in Garuda Purana -Chapter 50 -Verse 1 - Discourses on charities and gift-makings, etc.- See page No. 113 .
अहन्यहनि यः कुर्य्यात्क्रियां स ज्ञानमाप्नुयात् ।।
ब्राह्मे मुहूर्त्ते चोत्थाय धर्ममर्थं च चिन्तयेत् ।। Garuda Purana 50.1 ।।
Brahma Said : He who performs religious rites daily attains to Jnāna (knowledge). Having got up from bed at the Brahma-muhurta he should meditate on religious profit and worldly profit.
Now the next two verses gives us the idea what to do after waking up in Brahma-Muhurta. Its sid that a person should meditate and after that after completing necessary rites (daily routines related to body) , he should go to river for ritual bathing .And he should perform purification rites at the river i.e. Sandhya-Vandanam
चिन्तयेद्धृदि पद्मस्थमानन्दमजरं हरिम् ।।
उषः काले तु संप्राप्ते कृत्वा चावश्यकं बुधः ।। Garuda Purana 50.2 ।।
स्त्रायान्नदीषु शुद्धासु शौचं कृत्वा यथाविधि ।।
प्रतः स्नानेन पूर्यते येऽपि पापकृतो जनाः ।। Garuda Purana 50.3 ।।
He should also meditate, in the lotus of his heart, on blissful and undecaying Hari. When the dawn approaches a learned man, having performed the necessary rites, should repair to a river of pure water for bathing, and perform there duly the purificatory rite. Even sinful wights are sanctified by morning ablutions.
It is said in Garuda Purana that one should perform Achamana or libations of water to the sun .With Gayatri Mantra .
आचम्य विधिवन्नित्यं पुनराचम्य वाग्यतः ।।
संमार्ज्य मन्त्रै रात्मानं कुशैः सोदकबिन्दुभिः ।। 50.16||
आपोहिष्ठाव्याहृतिभिः सावित्र्या वारुणैः शुभैः ।।
ॐकारव्याहृतियुतां गायत्त्रीं वेदमातरम् ।। 50.17 ।।
Having rinsed his mouth he should do it again observing silence. Having sprinkled his body with drops of water through Kuśa reeds and with Mantrams, Apohistha, Vyarhriti and the auspicious Vāruni and having recited the Gayatri, consisting of Om and Vyarhriti, the mother of the Vedas, he should offer libations of water to the sun with his mind fixed in him.
So yes one can perform sadhana like Achamana , Pranayama , meditation , chanting of mantras , study of the vedas etc. at Brahma Muhurtha. Which we can read as described in that chapter.
We can also read this chapter from Wisdom Library site
Instead of personal practice i am herewith providing more general answer from scriptures.