I am only providing an answer of your below question.
What are the rules for these? Are there any texts which explicitly list out the rules to be followed by sanyasins ?
There are various Sanyasi Upanishads which talk about rules and regulations about sanyasi life.
1) Avadhutaka Upanishad
2) Jabala Upanishad
3) Turiyatitavadhuta Upanishad
4) Parabrahma Upanishad.
There is also Bhiksukopanisad which deals with the subject.
Here is excerpt from Jabala Upanishad.
VI-1. There are sages called Paramahamsas (as in the days of yore, the
sages) Samvartaka, Aruni, Svetaketu, Durvasas, Ribhu, Nidagha,
Jadabharata, Dattatreya, Raivataka and others, wearing no
distinguishing marks, with conduct beyond the ken (of worldly people)
and who behaved as though bereft of their senses though (perfectly)
Discarding all these, namely the threefold staff (of bamboo), the
water pot, the sling (to carry personal effects), the (alms-)bowl, the
cloth for purifying water (tied to the staff), tuft of hair and sacred
thread in water (i.e. a reservoir) by reciting Bhuh Svaha, the
Paramahamsa shall seek the Atman.
V-3. Then (in the case of those entitled to renunciation) the
mendicant monk wearing (ochre) coloured garment, with shaven head,
accepting nothing (excepting food for bare sustenance), being pure,
injuring none (in thought, word and deed), (austerity) living on alms,
becomes fit for realizing Brahman. If sorely afflicted (by disease,
etc.,) he may renounce the world by mental resolve, or by spoken words
uttering mantras. This way (of renunciation) has been prescribed by
Brahma (the creator, in the Vedanta); the ascetic (the Sannyasin who
has renounced the world) following this path realizes Brahman. Thus
indeed it is, O, revered Yajnavalkya (appreciated Janaka).
Yati Panchakamis a work by Adi Shankaracharya which speaks about as to how a Yati or a person who has realized the ultimate reality of Brahman and is completely detached to the world would behave in the world.
Yati panchakam or Kaupina Panchakam –
मूलं तरोः केवलमाश्रयन्तः| पाणिद्वयं भोक्तुममन्त्रयन्तः ।
श्रीमपि कुत्सयन्तः |कौपीनवन्तः खलु भाग्यवन्तः ॥ २॥
Sitting at the foot of a tree for shelter, Eating from his hands his
meagre portion, Spurning wealth like a patched-up garment, Blest
indeed is the wearer of the loin-cloth .
वेदान्तवाक्येषु सदा रमन्तो भिक्षान्नमात्रेण च तुष्टिमन्तः ।
विशोकमन्तःकरणे चरन्तः कौपीनवन्तः खलु भाग्यवन्तः ॥ १॥
Roaming ever in the grove of Vedanta, Ever pleased with his beggar's
morsel, Wandering onward, his heart free from sorrow, Blessed indeed is
the wearer of the loin-cloth
Shreemad Bhagvat purana also discusses the rules for Yati’s or Sanyasis. There is separate chapter about Rules to be followed by Sanyasis. SB 7.13
Here are some Rules and Regulations mentioned- :
बिभृयद् यदयसौ वास: कौपीनाच्छादनं परम् |
दण्डलिग्डादेरन्यत किच्त्रिदनापदि ||२||
bibhṛyād yady asau vāsaḥ kaupīnācchādanaṁ param
tyaktaṁ na liṅgād
daṇḍāder anyat kiñcid anāpadi
A person in the renounced order of life may try to avoid even a dress
to cover himself. If he wears anything at all, it should be only a
loincloth, and when there is no necessity, a sannyāsī should not even
accept a daṇḍa. A sannyāsī should avoid carrying anything but a daṇḍa
and kamaṇḍalu. SB 7.13.2
एक एव चरेद् भिक्षुरात्मारामोsनपाश्रय: |
eka eva cared bhikṣurātmārāmo ’napāśrayaḥ
The sannyāsī, completely satisfied in the self, should live on alms
begged from door to door. Not being dependent on any person or any
place, he should always be a friendly well-wisher to all living beings
and be a peaceful, unalloyed devotee of Nārāyaṇa. In this way he
should move from one place to another.SB 7.13.3
नासच्छास्त्रेषु सज्जेत नोपजीवेत जीविकाम |
तर्कान्प्क्षं कं न संश्रयेत ||७||
nāsac-chāstreṣu sajjeta nopajīveta jīvikām
tarkān pakṣaṁ kaṁca na saṁśrayet
Literature that is a useless waste of time — in other words,
literature without spiritual benefit — should be rejected. One should
not become a professional teacher as a means of earning one’s
livelihood, nor should one indulge in arguments and counterarguments.
Nor should one take shelter of any cause or faction.SB
नशिष्याननुबन्धित ग्रन्थान्नैवाभ्यसेद् बहुन् |
नारंभानारभेत् क्वचित् ||८||
na śiṣyān anubadhnīta granthān naivābhyased bahūn
upayuñjīta nārambhān ārabhet kvacit
A sannyāsī must not present allurements of material benefits to gather
many disciples, nor should he unnecessarily read many books or give
discourses as a means of livelihood. He must never attempt to increase
material opulences unnecessarily.SB 7.13.8
So it seems that there are various texts which are available on the subject you enquired , but I will also try search a exclusive book on Rules of sanyasis.