Yes, a person can still travel in the US even with a criminal record for trespassing. However, some countries may not permit entry with any type of criminal record.
Probably not, especially if you were under active prosecution for a criminal offense in your home country.
Question is unclear. Are you asking can you travel TO the US on a visa with a pending case, or can you travel FROM the US to another country with a pending court case. Either way the answer would be unclear. In travel TO the US, it would depend on the seriousness of the charge against you as to whether you were admitted or not. In the second instance, it wold depend on what the country you were travelling TO thought about your case as to whether they chose to admit youor not. For a more explicit answer you would need to call the embassy or consulate of the country you are asking about.
Define what is meant by "pending." If you are charged and released on bailbond prior to court action your travel may be (and probably IS) severely curtailed. As far as being allowed entrance to the PI; no government forbids entrance to holders of valid passports and visas for crimes they haven't been convicted of.
no
no
Yes .. pending court approval.
Yes travel agents do charge their fees for work done.
Yes
yes you can
No
Yes or no is the answer.