Do you think women (or in particular that woman) can guess my feelings (or to some degree)? By my feelings I also mean being a transgendered person.

Long story short: in the lab where I'm doing my PhD among the girls there is one (call her "M") who is very self – centered and would "step over a dead body" to reach her goal. Needless to say we aren't in the best of terms – although I try to be neutral. 
A few days ago out of the blue she asked me how I felt, if I was happy and also told me she would like to know me "closer" and "more as a friend". (How I feel? Are you kidding me? It's so confusing even trying to think how to explain without getting into details). I just told her my feelings are everywhere (or something like that). She continued following days saying I "owe her an answer". Up to this point I have ignored her.

Over the past year there has been some change in how I present (somewhat long hair instead of crew cut, wearing girl jeans – not anything frilly,  a couple of times wearing clear nail polish and "pal talk" with another girl ("D"). I haven't come out yet. Still, to some people it may be obvious I'm hiding something - not letting myself be actually me.
I was just wondering (not that it makes any difference) why the heck would that girl (M.) ask that thing. I told "D". about this (we talk about things as friends and I've expressed some "girlish" (kinda?) interests to her – talks about nails, about how I like what she's wearing, once ended up talking about prices in jeans) and she concurred that "M." is only kind when she needs something.

Imo its not rocket science.
If people change its perceivable, people give different vibes, have somewhat different looks, etc.
Sensible persons and people who listen to their intuition can pick this up.

Well why she asked you is another question... its up to you to find out.
Its possible she wants something, its also possible she sensed a change in an environment where she likes to know what is going on.

Well one possible answer would be to say you changed a bit... having some new hobbies or whatever...
or you feel more relaxed lately...
well its up to you how to react...

you don't "owe her an answer" to anything. not sure how the whole "lab , working on a phd" situation works ? if it's has structure sort of like a job I'd be careful of divulging to much personal information to a person you describe as willing to step on anyone to further her cause. you can be friendly in a work setting type manner but proceed with care.....

I'm doing my PhD (plant- molecular biology) and it's mainly lab work at the university. Obviously I don't owe her an answer and sure as heck I'm not going to tell anybody about this, much less her. I know that since I still have one year + to finish, still not doing anything related to transition (financial issues) I can't tell anybody over there.

I know I may give out hints (based on what I'm wearing and maybe some other cues) but currently I can't tell anybody.
If theoretically I told somebody (even "D.") I can't risk how she would react and pretty sure the news WOULD spread out (it's hard to keep such a secret to oneself).

Gossip is a currency.  She might be mining.  She knows the brand and the cut of the pants you wear.  Women know clothes brands like men know car brands.  She might have caught on from the nails -- working in a lab, aren't your nails fairly visible?  My nails are extremely broad, so when they're polished they're huge and shiny and extremely obvious, even with clear nail polish.

Remaining silent is a good idea but you might be able to make her uncomfortable for asking. Under normal conditions women view men a sexual predator or a sexual conquest. You might ask her which of the two she views you as. It is also possible that she is a climber and wants to use you as a stepping stone to the next level. She hasn't told you what she wants or suspects so she is giving only the "promise" of friendship for what she will gain.

I wouldn't even consider dealing with her until you understand what she wants from you.

I think Sparrow is on the right track.  'M' suspects you are either gay or trans and in the closet.  This puts her in a position of being able to do you harm.

I don't have any suggestions for how to manage the situation.  It does not sound like coming out pre-emptively is in your plans.  But you might want to consider how you will handle the situation if she "outs" you.