You can give Mishloach Manos throughout the year – there’s no issur! The question is whether you’re yoitze with the mitzva of umishloach manos is lereau.
Once the taanis is over and you have heard the Megilah it is no longer Taanis Esther, you are officially into Purim. So you are allowed to give Shalach Manos at night already.
If I am not mistaken, mishloach monos must be done during the day, not at night and certainly not on taanis Esther. At those times it is a nice gift of food but not yotzei
You CANNOT be yotze the Mitzva Meshloach Manos at night, nor can you give Matonos L’Evyoinim (unless you are giving it to a person who will give it to the evyon during the day) nor can you be yotze the Seuda by night. All these mitzvos need to be done during the DAY!!! ONLY!!!