I see the original question as been modified when I went online again. The original question included "hinting/asking"
I have included this under wrong livelihood.
How to know who is a good monk is a little more difficult to know than who is a bad monk. People will judge differently on what factors makes one a good monk. We can start with morality according to the monks rules which he has an obligation to follow. There are a few easy signs that one is a bad monk.
When he goes out into the village, if he has one shoulder exposed, this is a very clear sign that he breaks most of the rules. If he has both shoulders covered, that means he follows this rule, but maybe not others. This is just a quick way to throw out the majority of monks into the bad monk pile. Unfortunately, most monks in Myanmar break this rule and that also means that most monks break most of the rules.
Monks need to follow all of the rules 227 rules and also the rules in the Culavagga and Mahavagga. Likewise, they need to follow according to the commentaries as well in most cases.
Most Western Bhikkhus do not like the commentaries. That is where "interpretations" can come.
Most of the information below, is from the BMC The Buddhist Monastic Code
Summary:
A Bhikkhu cannot use money.
A Bhikkhu cannot point out a kappiya without someone asking, "Who is you kappiya?"
A Bhikkhu cannot accept envelopes presumably with money inside. It is an asannya offence (in the root text). Which means, no perception is necessary for it to be unallowable. That means the monks should not be intentionally ignorant. The BMC debates and allows the modern use of "checks."
A Bhikkhu cannot ask for things from "Just anyone". He needs an invitation from a non-family member ( blood relation)
A Bhikkhu cannot hint to "Just anyone" (as above)
A Bhikkhu cannot do the above for another bhikkhu(s) either.
The BMC says checks are not money but a "promise to pay." Sri Lanka and Myanmar Vinaya traditions call this money. Money is defined as anything accepted as used in trade. A US dollar is a mere bank note too. Google "A Life Free From Money pdf"
The same as above is judged with signing checks.
A bhikkhu can ask for a bowl from anyone if it is broken or stolen.
A bhikkhu can ask for a single robe from anyone if he is left with only one (of three).
A bhikkhu can go for alms in the evening for "extra items," usually medicine or oil for light. The donors will offer food and he will refuse. Then the person may ask, "what do you need?" Then he can say.
Lay people or committees can ask "just anyone" for things or money, etc. for monks if it is their own idea. This might be what you are seeing on brochures and websites, etc.
A Bhikkhu cannot ask his helper, committee etc, to ask others for money for himself.
A bhikkhu must be invited by a committee or kappiya before he asks them for things.
The above list is followed correctly unfortunately by a small minority of monks, known as vinaya monks, or forest monks. Often the other (majority) monks do not know what proper behavior is. They may memorize the rules, but do not think it is something to be practiced since corruption is so wide spread. One of my monastic friends told me he cried when he found out that he was never supposed to touch money. A monk may purify himself at any time.
Often, they just do not know.
Traditions often have interpretations which makes items seem "allowable.". Sometimes this is allowed and sometimes one can just be fooling oneself. In the end it is up to them. Often bhikkhus do not reflect or question questionable practices in a tradition because of the wide spread use. Money and medicines are often such topics.
"Monks, strive with heedfulness. Rare is it that Buddhas arise in the
world. Rare is it that [one] it that [one] obtains a human [birth].
Rare is it to have the good fortune of [being in the right] time [and
place]. Rare is it [that one has the opportunity] to take the Going
forth. Rare is it [that one has the opportunity] to listen to the
True Dhamma. Rare is it [that one has the opportunity] to associate
with good people." (c.f. D.32.33 & A.8:29)
BMC I, 2009 ed. pdf
Monks must also practice right livelihood according to not doing things from the list below:
Wrong Livelihood The Cullavagga, in a section that begins with the
same origin story as the one for this rule (Cv.I.13-16), treats the
banishment transaction in full detail, saying that a Community of
bhikkhus, if it sees fit, has the authority to perform a banishment
transaction against a bhikkhu with any of the following qualities:
1) He is a maker of strife, disputes, quarrels, and issues in the
Community.
2) He is inexperienced, incompetent, and indiscriminately full of
offenses (§).
3) He lives in unbecoming association with householders.
4) He is corrupt in his precepts, corrupt in his conduct, or corrupt
in his views. 5) He speaks in dispraise of the Buddha, Dhamma, or
Saṅgha.
6) He is frivolous in word, deed, or both.
7) He misbehaves in word, deed, or both.
8) He is vindictive in word, deed, or both.
9) He practices wrong modes of livelihood. This last category
includes such practices as:
a) running messages and errands for kings, ministers of state,
householders, etc. A modern example would be participating in
political campaigns.
b) scheming, talking, hinting, belittling others for the sake of
material gain, pursuing gain with gain (giving items of small value in
hopes of receiving items of larger value in return, making investments
in hopes of profit, offering material incentives to those who make
donations). (For a full discussion of these practices, see
Visuddhimagga I.61-82.)
c) Practicing worldly arts, e.g., medicine, fortune telling,
astrology, exorcism, reciting charms, casting spells, performing
ceremonies to counteract the influence of the stars, determining
propitious sites, setting auspicious dates (for weddings, etc.),
interpreting oracles, auguries, or dreams, or — in the words of the
Vibhaṅga to the Bhikkhunīs' Pc 49 & 50 — engaging in any art that is
"external and unconnected with the goal." The Cullavagga (V.33.2)
imposes a dukkaṭa on studying and teaching worldly arts or hedonist
doctrines (lokāyata).
For extensive lists of worldly arts, see the passage from DN 2 quoted
in BMC2, Chapter 10.
BMC I Lists wrong livelihood extensively starting on page 518 PDF ed.
"Medicines"
There are some things in the BMC which I think are very misleading, especially concerning, "medicines" and how "Any Reason" is defined (p232). I could not find any pāli evidence that mentions "hunger and fatigue" as a valid medical reason. I could be wrong, but I asked a couple of knowledgeable monks to verify this and they also agreed with my findings. This would exclude many things which are considered medicines.
I will not cover further with lists of the "medicines." Only that there should be a valid reason for taking them and justifying their use after Noon.
The reflection and criteria are below. It is in every monastery chanting book and should be chanted every day. (Nauyana chanting book source)
"Medicine Reflection"
Whatever requisite of medicine for treating illness has been used by
me today without reflection was only to ward off painful feelings that
have arisen, [and] for the maximum freedom from disease.