'do rzeczy' means "know what s/he wants", "self-assertive (in a good way)" etc I'm reminded of how an American woman once interviewed for a job where I worked... my boss approvingly called her "Baba do rzeczy" and employed her (unfortunately we couldn't compete price wise with her other jobs).
Oh dear, another one I've not much idea about. A couple of guesses: Is it similar to twisting somebody's arm- to pressurize someone into doing something they don't want to? Or something is convenient for somebody?
Nope. To do means to serve sb, like in the office, for example. From hand means to do it instantly, without waiting in the line. Załatwić kogoś od ręki.
What situations are called Mexico/ Saigon by Poles:?
IIRC "Sajgon" refers to a place that's ben wrecked and "Meksyk" refers to general disorder... I haven't heard either in a long time.
One odd thing I think was/is the frequent use of the term "Mexico City" in Polish since Mexico isn't an English speaking country... but I haven't noticed Miasto Meksyk being used as frequently, much less Ciudad de Mexico or Distrito Federal ('federal district' which is what people in Mexico usually call it)
Yes, that is quite correct. Simply speaking, under cover. I was sure I wrote coatling - płaszczyk - but now I see it is coating, still close but not what I really meant.
Ones of disorder and confusion?
Yes. Also chaos or even violence. I think Mexico idiom comes from Kraków. Meksyk was a bar in Nowa Huta District in communist times and it was infamous for rough customers, heavy drinking and frequent fighting. Saigon bears an obvious reference to the Vietnam war.