The "-tır" is actually the optional suffix for 3rd person singular. (He/she/it is).
So why is it singular? I think that Turkish avoids the plural if at all possible. E.g., "two books" is "iki kitap". There's no plural ending to the noun, because the number already establishes that we're talking about more than one. Same here with "şunlar", which makes it clear we're talking about more than one.
It can be quite counter-intuitive, especially because in other cases (e.g., when using the possessives) matching the suffixes is very important.
I can now see why early Hungarian scholars thought their Uralic languages and the Turkic languages were related, since in this, as in so many other grammatical features, they are similar. Essentially, Hungarian avoids the plural wherever it is not needed for clarity, as after numbers (két könyv, rather than két könyvek).
Yes, for translational purposes they are synonyms. In usage one would use 'şu' while pointing towards the object and use 'o' while talking about the object in general.
For example one can point to the fish and ask someone 'Su baliklari yer misin?', and the person replying would look at the person who asked the question and reply 'Evet, o baliklari yerim'.