This is a conventional way of numbering trains in Russia, Kazakhstan, Belarus, Ukraine and etc. Passenger trains have number consisting of 3 digits and a letter. Letter allows to distinguish trains with same numbers, e.g. 001A = St.Petersburg - Moscow; 001B - Moscow - Minsk; 001M = Vladivostok - Moscow, etc. Well, it's hard to say, why the letter Щ was chosen
Yes, the letter is only assosiated with destination. Moreover, usually it's just an information for official use. I have never heard the letter been announced at stations for ordinary passengers. Train type is defined by digits in its number. E.g., trains numbered 001 - 148 are fast trains, 151 - 168 - high-speed ones.
Thanks for the answer. What is the price difference between Regional (R), InterRegional (IR) (fast) and other trains (IC, express etc.)? For example, in most of Europe the prices are the same for R, IR and IC, the only difference beeing the seat reservation or a small difference (for ex. in Hungary is about 230 HUF for 250 km, that means about 0,8 eur, the price of a tram ticket in Budapest). In Romania, the price of IR is aprox. 2 x price for the R and the price for IC is aprox. 3 x price for the R, although there is a very small time difference between IR and IC (maybe 10 - 15 min for a 600 km ride).
Well, as we have different system of division trains into types here, it might be difficult to compare them correctly, but nevertheless I'll try. Let's take route from Moscow to Rostov-na-Donu (about 1220 km ride) as an example. There're three main train types: ordinary passenger, ordinary fast and special fast (or Premium). Prices for the 2K class (which means four-berth compartments without extra service) are: 2905 RUB (~ 73 EUR) for 25-26-hours trip in passenger train; 3161 RUB for 20-22 hours in fast train and 4737 RUB for 17-18-hours ride in Premium class fast train. So in this case we pay much money for comfort and speed. On the other hand, if we look at Moscow - St.Petersburg line (650 km), we have the following figures here: about 2600 RUB for high-speed train (Sapsan flies this distance in 4 hours - daytime services with seating places only); 2886 RUB for place in compartment in Premium-class fast train and 1927 RUB for simple fast train. Both ordinary and special fast trains run for about 8 hours (some ordinary are in fact faster, than special). So in this case we pay extra money only for service, comfort and convenient departure/arrival time, but not for speed and time saving.
The letter in "Express-3" ticket system usually designates the railway, which owner of a train. Rare exceptions. "A" is Oktybrskaya railway RZD, "Г" is Gorkovskaya railway RZD, "E" is Sverdlovskaya railway RZD, "M" is Moskovskaya railway RZD, "H" is Zapadno-Sibirskaya railway RZD, "П" is Yugo-Zapadnaya railway UZ (Kiev), "T" is former Alma-Atinskaya railway KTZ, "Ф" is Uzbekistan railway, "Ц" is former Tselinnaya railway KTZ, "X" is former Zapadno-Kazakhstanskaya railway KTZ, "Ш" is Odesskaya railway UZ, "Щ" is Kyrgtzstan railway etc. I don't know all letter.