I have an opportunity to do business with a customer from Taiwan named 'Wei Keng Ho'. That is all the information that I have. Is the name male or female? And is it likely to be Chinese name ordering or Anglicized ordering? Is my best guess to start the letter with 'Dear Mr. Wei' or 'Dear Mr Ho' ? Or is there some ambiguous but polite way of writing the salutation?

I really need to do this today, so a quick answer would be much appreciated.

any more than you would be if you got "Mr. or Mrs. Banbeck".

My dad once got a letter from one of his German relatives addressed to "Mister and Misses [his name]".

At least it wasn't "Mister and Mistress".

Would it be rude to begin with "Dear Wei Keng Ho"?

(Or are we laughing at the spelling of "Mrs."?)

This. There's a difference between "Mrs." (there's a word "Missus" for a wife) and "Misses" which makes it sound like Dad's cavorting with multiple unmarried women.

It is rare for Mrs. to be written in a non-abbreviated form, and the word lacks a standard unabbreviated spelling. In literature it may appear as missus or missis in dialogue. A variant in the works of Thomas Hardy and others is "Mis'ess", reflecting its etymology. Misses has been used but is ambiguous as this is a commonly used plural for Miss.

from Taiwan named Wei Keng Ho

I'm a little bit late to reply to Joaz Banbeck but chinese names are usually expressed [lastname (one character) - firstname (one or two character(s))].

Out of curiosity - is it always hard to tell what is the first and what the last name of in that language?

If the name is written in Chinese, then in most cases it is pretty clear.
The problem here is that it was written in English, and the name ordering
is different between English (Given name first, then Family name)
versus Chinese (Family name first, then Given name).
('Family name' and 'given name' are less ambiguous than 'first name' and 'last name'.)

Same problem in Japanese. For example, the cover of The 21st Century Dictionary of Basic Joseki
says "by Takao Shinji 9-dan", but the first page inside says "by Shinji Takao".
So someone not familiar with Japanese would not be able to tell based on these two pages which is which.

Another issue here is the Taiwanese anglicized convention is different from pinyin.

Joaz, it's been almost 2 weeks -- have you found out the actual name (in Chinese) yet ?

I really find that interesting.

From what I know, looking at names of some Japanese pros, it is often also easy. For example: Kato Masao... since I know of a few 'Kato's I assume Kato is the first name. Same with Toshiro Kageyama, and so on. With many names I have no clue, but I always assumed this is because I am unfamiliar with the language, and for somebody speaking Japanese if would be immediately apparent which part of 'Otake Hideo' is the first name and which is the last name, regardless of which order it was written.

I really find that interesting.

...

However, what I wondered about was more if there are any other ways to tell first names from last names.
...

In most of cases the last name contains only one character and it can be looked up in the list of common surnames. The rest two characters are the first name. So in the case of `Wei Keng Ho', the first name is Wei Keng, the last name is Ho.

There is Double-barrelled name, but not common as the example described above in Taiwan (Don't know the current situation in China.) With this case, the first few (usually two or three) characters generally be the last name, the rest are the first name.

The characters here indicate Chinese character.