Don't go to any trouble on my account - I was just being lazy in asking

when translated using www.translate.ru (which uses the Prompt translator - I think the site is owned by them?) gives
   
Не идите ни в какую неприятность на моем счете - я только был ленив в выяснении!

Not bad, but it sees the word "go" and wants to translate it with a verb of motion... the final result involves the user not going on foot to the trouble.   I would personally have translated it "Да не замучитесь ради меня", which is the usual way of "going to trouble for something".

The vodka is strong but the meat is rotten

How is our Russian online translator on that?

Водка сильна, но мясо является гнилым

Not bad, correct but not stylistic. Vodka is rated крепкая ("strong") and not сильная ("powerful" - it relates to political or military power) in Russian...  the result is understandable but clearly not completely right.  The only way in which a vodka might be сильная is if it was driving other brands off the market.

There might not be! They wouldn't use one in a Russian version of that kind of sentence (unless I'm mistaken ... Reiner?).

You're bang-on, Tinners :-)  The verb "to be" only exists in the future and past tenses (and compounds of those) in Russian.  In the present tense it's completely omitted, and there isn't even a theoretical unused form of it.

I'm a student - ya student
I am English - ya anglichanin (or ya anglichanka if you're female)
Ona violonchelistka - she's a cellist

If the crux of your sentence hangs or falls around the existence of something (or not), you have to use a different verb viz:

Petersburg was the capital until 1918, but Moscow is the capital now - Piterburg byla stolitsa do 1918 goda, a Moskva yavlyaetsya stolitsy seichas.  [literally "but Moscow is known to be the capital now"... "capital/stolitsa" has to go into the instrumental case as it's the "result" of a reflexive verb second time around. You can see the past tense of "to be" in the first half of the sentence, "byla"] - that's all fine and dandy.]

As an interesting social phenomenon, many people will "reach out" to put a present-tense verb into phrases about whether things are or not, and in place of the verb that doesn't exist will say "eto" ("this/that")...  usually when tempers are fraying, if making a point.  I heard a student angrily demanding the student discount for admission to a Jackson Pollock exhibition last weekend: "A ya eto student!" she said, banging her student-card on the cash-desk window.  Similarly the airline staffer who was controlling the boarding of my flight Krasnoyarsk-Moscow last week held back the crowd to board some OAPs ahead of the throng. "Podojdite pojaluista! Eto pojilie liudi!".  ("Wait, please! These are elderly people!" LIT: "That - elderly persons!")

(I've done these all in transliteration, for those who aren't comfy with cyrillic or may not have the fonts installed).

PS in addition to not having "to be", we don't have articles (the/a/an etc) either   "I - Englishman!".  Heap good, eh?

I don't think it's a nuisance - actually it's very convenient   'I pianist' - simple as that

There's no verb 'to go' either.. you walk, ride, skate, run, drive etc.

And there's no verb 'to have'. 'By me there bicycle', 'by her there mobile phone' etc.

There are two different verbs for 'putting something on a table', depending on whether they lie flat or stand upright. Plates stand upright (apparently).

There is a test next week, so write it down