I'm not a lawyer. Here is the laymans understanding.
MO recognizes permits from ANY state.
You still can't carry anywhere Federal Law prohibits.
MO has a list of "prohibited places". It is not a crime to carry there, but...
If you are asked to leave, do so, and do not argue. If LE are summoned, possible fine, etc. This included businesses and private properties that are posted.
Required to show permit on demand of LEO, penalty is a fine if you do not.
OC: Permissible at state level. However, local laws may regulate open carry.
"Concealed Carry" includes the carry of other legal (in MO) deadly weapons concealed on or about the person. However, only firearms are specifically "off-limits" to local regs.
Of course, you should verify all this yourself, or contact an actual attorney.