1)I just want to ask a person if he understands what I am saying(for ex. in English) and politely ,too.
I Longman LDOCE dictionary there is an entry
"do you understand?
spoken used when you are telling someone what they should or should not do, especially when you are angry with them ".
I was not angry at all at that moment etc. So how to ask the question politely?
It's a bit misleading. It largely depends on intonation. The way in which the question is said will show if the speaker is displeased or not.
You could easily say to someone "To get to the doctor, you go along this street and turn right. Do you understand?" and it will merely be checking that they have understood your directions.
On the other hand, your small son may be being disobedient, so you say "If you do that one more time, you will go straight to bed. Do you understand?". Your voice will be stronger and it will be clear that you are angry.
2)does "underpin" mean corruption or bribery? No - it means to make sure that something is well-founded.
3)what is the meaning of "unappreciated"(is this correct?:Software is unapppreciated in today's China.) un-appreciated - not appreciated.
Thanks for help in advance,