As a Buddhist, is it right to say that anything about Buddhism is right?

The short answer is "yes". Following the Eightfold Path implies striving to understand and distinguish right from wrong and true from false. So of course Buddhist traditions have a lot to say about epistomology ("What is true knowledge?") and about ethics ("What is good behavior?").

It really depends upon what you mean by 'Being a Buddhist'. In the book 'Buddhism plain and Simple', Steve Hagen says that the more and more I am a Buddhist (i.e. practise the Dhamma) I know that I am not a Buddhist( meaning the sense of self disappears). So by being Buddhist if you mean one who practises the Dhama as taught by Lord Buddha then 'yes', its safe to assume 'any thing about Buddhism is right'.

But if by being a Buddhist you mean just a connotation, i.e. for political or socio economic reasons for e.g. you call yourself buddhist because your parents were buddhist and their parents were buddhist and entire Myanmar is buddhist and none of you are practising anything said by the Buddha...then your actions are upto your own scrutiny.

The sense of religious identity is a very twisted matter.

Insted of calling your self a 'Buddhist' as in this context in which you are asking the question, ask the question that,

As somebody who follows the dhamma taught by the Buddha...

Then the answer is yes, yes, yes...

The dhamma is like a dew drop or honey sweet in the begining, sweet in the middle and sweet at the end.

As a Buddhist, is it right to say that anything about Buddhism is right?

I assume that "right" might have any of several different meanings:

1. A correct or truthful, beneficial, description of the world and its processes
2. Noble, or ariya
3. Better than other people or beliefs

The first ("truthful, beneficial") is a broad subject:

• See the Kalama Sutta for example -- if Buddhism consists of doctrine which you know yourself to be true (sandiṭṭhiko, akāliko, ehipassiko, opanayiko), praised by the wise, it's hard to see how that could be wrong
• It's a broad doctrine -- being prosperous, prudent, and kind if you're a layperson, perhaps other ambitions (including nibbida) if you're ordained -- it's so broad and detailed that it's difficult to understand, or it may even sometimes seem self-contradictory in places, or consisting of truisms (e.g. "do what is skillful and don't do what leads to suffering")
• Whether you believe it's right, emotionally feel it's right, may depend on finding and seizing a specific aspect of it -- for example, "yes, Buddhism really speaks to me about dukkha, it's got that right"; or, "yes, Buddhism is really kind and harmless, isn't it, that's something I can really admire"; or, "yes, the Buddha is definitely the best person I've ever heard of" -- but some people don't see everything as dukkha, some people might see pacifism as some un-energetic failure, etc., so (for whatever reason, maybe many reasons) it doesn't seem right to them
• It's arguably unreal unless it's actually practised -- it exists in the mind of the beholder, and (perhaps like Mathematics) it's kind of meaningless (even if other people find it predictive) when you're not mindful of it.

The second ("noble or ariya") I've not much to say about -- bits of Buddhism or doctrine are ariya by its own definition.

The third ("better than others") is difficult to generalise about. I expect stream-winners have a clear view of what Buddhism is (before that it's difficult to be sure of what you're talking about). According to this answer, making comparisons is a form of "conceit", and only a stream-winner will only give rise to true conceit i.e. true comparisons.

If it is not right to say so, how right or wrong is it to assume that?

I think you're asking, "If it's wrong to say so is it alright to assume it?"

Firstly I think that whether it's right or wrong doesn't depend on whether you say so.

Still there may be circumstances (perhaps when you're working with someone, and therefore busy with something else, or not wanting to proselytise when that's not welcome) when it's inappropriate to say so.

If it is wrong to say so, it may be wrong to assume it.

And according to some doctrine -- e.g. Paramatthaka Sutta (SN 4.5) -- I think that views themselves, attachment to views, seeing a view as supreme, is itself a kind of fetter.

Myself as a "traditional Buddhist" from Myanmar, I find it pretty disturbing to see Buddhists here having blindfolded faith in Buddhism and every act of monks and religious leaders.

I guess that's so, yes. Living in the West, here, I haven't seen many monks in person, nor acting as leaders -- and I haven't seen any who seem to be misbehaving -- but I do see news, sometimes, interviews, where a monk seems to be quite hostile for example, which I find strange -- like a lot of news though that might be exceptional, news tends to report on what's scandalous rather than on what's normal, which can lead to a false (or extremist) impression.

I did read a booklet called The Broken Buddha once, so I hope I don't have a false (over-idealised and blindfold) view of modern society.

This book, Broken Buddha, although critical of much of what goes on in some Sanghas, could help provide some valuable information for some aspiring monks so that there are no unreasonable expectations.

I suppose some people might say that Buddhism is in decline, or perhaps was even lost after the first few hundred years -- I don't think so, I suppose that even at the time (which the suttas talk about) there was a variety of people.

Still, I like reading, too, to understand what the ideals are.

as a self-aware Buddhist, how can you analyse if your thoughts or actions are right, without having much knowledge about Dhamma (Dharma)?

I think that maybe, without a knowledge of the Dhamma, you can't (determine whether your thoughts are right and wrong) -- that's a reason why you might (or should) want to know more about Dhamma.

• People have recommended several books (e.g. here and here and here).
• There are suttas (each is shorter than a book)
• There's the Dhammapada (each verse is shorter than a sutta).

There are some rules of thumb, for example ...

All mental phenomena have mind as their forerunner; they have mind as their chief; they are mind-made. If one speaks or acts with an evil mind, 'dukkha' follows him just as the wheel follows the hoofprint of the ox that draws the cart.

... so you might try to avoid doing anything with "a mind of hate", for example, e.g. motivated by revenge.

Apart from literature, people recommend you practice (actions, e.g. generosity and ethical behaviour; and meditation); and that you should have "good friends".

There's two little bits I find helpful, to "know what's right without having much knowledge about Dhamma".

• One is that some of the suttas conclude with the Buddha's saying, "Both formerly and now, what I teach is dukkha and its cessation."

  There's a children's game where you have to guess where some object is, that someone else is thinking of -- so you walk around, and as you do they say "you're getting colder" if you're moving away from the object, and "you're getting warmer (or hotter)" when you move towards it ... until eventually you put your hand on it.

  Similarly if what you're doing is increasing dukkha then maybe that's not right, conversely if it tends toward cessation (of dukkha, of craving, and attachments) that may be closer to what the Buddhism of the Pali canon has in mind.

• The second bit of doctrine that I think it's helpful to know about or keep in mind are the Brahmaviharas:

  These four attitudes are said to be excellent or sublime because they are the right or ideal way of conduct towards living beings (sattesu samma patipatti). They provide, in fact, the answer to all situations arising from social contact.

  The Brahma-viharas are incompatible with a hating state of mind...