Russian grammar is actually extremely straightforward compared to, say, Latin. If this is your first declension/conjugation language, that isn't Russian's fault.
The Slavic languages as a whole evolves to be relatively easy to learn, as they were a regional trade language before they split apart, and for a time afterwards too.
I thought the ending ы made the word plural?
It does (well, depending on other things). But it's also the singular, genitive ending for feminine words ending in "а".
And in this construction "У" always takes genitive.
It just so happens that the genitive plural of "женщина" is "женщин", and preposition "у" requires genitive.
In fact, I believe any noun ending with "-на" simply loses the trailing "a" in its plural genitive form -- at least all examples that come to mind fit this pattern.
To add to what an_alias has said:
-а | drop a
I wish it were that simple (and I am saying this with a degree of sarcasm). There are certainly exceptions to that rule. I am not a grammarian to tell you the pattern, but certain examples come to mind: овца (sheep) → овец, дырка (hole) → дырок, марка (postage stamp) → марок etc. Now that I think about it, all (or almost all) words ending with -ка change to -ок unless -ка is already preceded by a vowel (строка [a line of text] → строк, река [a river] → рек). But as the first example shows, those are not the only ones acquiring and extra vowel inside, basically for easier pronunciation. All of them drop the trialing -a though, so that part of the rule certainly stands.
I wrote "the lady has a brother" and this was marked as incorrect. I understand in English "lady" and "woman" have different connotations in relation to social standing, but they are essentially the same thing. I was just wondering if this distinction is more significant in Russian?
How come it is forbidden to use есть in "у слобаки нет вода' but it's O.K without the negation?
This has to do with the fact that нет and есть are linked words. Basically, 'нет' is the antonym - or the opposite - of есть. So нет = 'not есть'. By saying 'нет есть', then, you are literally saying 'not not is' or 'it is not not there/existing'.
"That palmtree is not not there!" Which will have your friends going "..? What're you on about, mate?"
Are you sure "не есть" would take nominative? The past and future are "не было" and "не будет", which also take genitive. Certainly if it's not a contraction of "не + есть" there are a number of sources that need to be corrected...
Some research (i.e. some Wiktionary) suggests that the contraction took place in Old East Slavic and the phrase in modern Russian would actually be "не есть тут".
Actually, I'm learning Russian for fun experience. I don't live in Russia and I'm not sure if I might have a chance to visit there either, though it would be lovely if I could. So I don't think I'll be reading any Russian newspaper or have a need to read one :p . If I can verbally communicate with someone who speaks Russian that would be good enough for me :) Who knows, I might change my mind in the future.
i also think that you have to learn the alphabet, some of the sounds in russian don't even have accurate equivalents in english. its not easy, but just getting the basics and then doing duolingo you can get a grip of it pretty quickly. i even managed to get the basic layout of the russian keyboard after completeing 5-6 units
In the future you can use this site to convert both ways between the Latin and Cyrillic alphabets (I actually have a hard time reading Russian written in the Latin alphabet so I use it when that shows up in the comments).
But for now:
Assuming zhenshhina isn't irregular and I got the genitive plural right I believe it's:
u zhenshhin est' brat
That's easy, there is a spelling rule to never write the "ы" after the letters "г", "к", "х", "ж", "ч", "ш", "щ", so it always would be "и" after them.
(Later you might encounter some exceptions to that but they are very rare and it's usually foreign names or terms, or made up words so don't worry about it now)