I would like to find informations on the quality and seriousness of a
Bank called Rietumu Banka located in Latvia. I know everything about
the bank itself but would like users opinion or reviews, and facts
about its trustworthiness.

Even supposedly reputable banks can and do go bottom up on occasions
but this is more likely in a country where the banking system is not
properly 'regulated'.

Without knowing, I suspect that Latvia may fall into this category.

Here in the UK, small depositors are given some comfort by Government
backed guarantees.

I suggest that you should first take a look at the banking system
itself because unless this is reasonably sound any opinion on an
individual bank may not be very helpful.

My father has an account in Rietumu Banka for several years now. His
only complaint is that it has significantly less ATMs than other,
competing banks in Latvia.
Only several banks in Latvia are locally owned, most belong to
Swedish, German etc. banks (e.g. Unibanka belongs to Skandinaviska
Enskilda Banken, Nord/LB Latvia to Norddeutche Landesbank etc.). This
foreign ownership is one of the reasons why the Latvian banking system
is generally considered very stable. However, Rietumu Banka is one of
those few banks that are owned privately and locally.
About the Latvian banking system - I wouldn't agree to
probonopublico-ga, actually nowadays it is very well regulated. I
personally would have no problem in entrusting my money to Rietumu
Banka, however, given the choice, I have chosen a larger bank with
more branches, more ATMs etc.

I found a poll about how people feel about Latvia's banks, including Rietumu Banka:
http://www.financenet.lv/sectors/bank/index.php?id=77308
If it's useful to you, I could translate the parts that are about Rietumu Banka.