Hi Kolopaper,
I can help you a little on your first question. Once you have placed your teleporter on your map and made it global, you must place a point trigger to the area you want the teleporter to take the player to. Make it global and give it a name you can remember.
After that, open the sidebar for your teleporter. Scroll down to the "Item State" section. The third line should say "OnUseActions." Click on the "..." button on the right hand column of that line. A new window named "Actions" should open up.
On the top left hand side, you should see a drop down menu, a green add button, and a red delete button. Open the drop down menu, select "Teleport," then click the add button.
The right hand side of the window should now display additional information. The bottom section (TeleportTarget) should have 3 lines: Target, m_Target, and m_Type. It should be default, but make sure m_Type is set to "Trigger."
Now click the "..." button on the right hand column of the Target line. A new window should open called "Select Global object..."
Click the Trigger radial button on the top. Then open the drop down menu right below and select the level that the trigger is located. The section right below the drop down menu should now be populated with all the triggers from the level. Select the one you made for the teleporter and click "Apply."
Now the right hand section of the "Target" line should be the same, but the m_Target line should have a string of something that looks like gibberish. This is actually the ID of the trigger. You won't see the name displayed anywhere.
If you really want to make sure that the teleporter is leading to the right trigger, write down the value of m_Target. Then go back to your trigger, select it, and open the side bar. Under the "Base" section should be a line called "GUID." Whatever your wrote down should be identical to its value.
Now when your testing character clicks on the teleporter, it should work. This is also how you get the doors leading upstairs/downstairs houses, wells, caves and holes and so on to transition to another area.
Unfortunately, I haven't looked into the teleport button from the UI and how it works, but hopefully this is a good starting place for you. Good luck!