In Platinum, it is fly.
Beat the 5th gymleader and leave the gym
It allows you to use the Cut HM. You get it shortly after by rescuing the Farfetch'd in Ilex Forest.
he is in the burned tower
Firstly, you''l have to defeat Chuck, the Gymleader at Cianwood. His wife, who is just outside the gym, would give it to you when you talk to her after defeating Chuck.
If you surf across the sea, you'll reach an island where a pharmicist has the needed medicine
The 15th gymleader Blaine is on the Seafoam Island, which is east of Cinnarbar.
Fly is HM2, surf to Ciawood City and beat the gymleader Chuck. After beating him, woman outside of the gym gives you HM2 - Fly and you can use it right away.
The 4th Gym witch is in Ecruteak City. He uses ghost type Pokemon.
No, there is not.
There are 2 Team Galactic bases. Veilstone city and the one you are I assume referring to in Eterna City. NW corner, but you'll need the HM cut as someone's move in the party. HM cut given by Cynthia after visiting statue and you have to beat the gym here to be able to use it on trees and enter the building.
You have to ask your mom for it after the 4th gym badge
I don't now