when you do trigger_teleport it automaticly, No matter what it is (to my experiance so far) invisible ingame - so what would have to do would be to say make the teleport part slightly at least larger. than just make a copy of whatever you want as a teleporter and put it inside that, i would use the trigger shader to be safe though.
(hoping that i helped

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As for the second part. do misc_teleport_dest and place that where you want your teleporter to teleport to, press n to open the entity window and at the bottem left you can use the circle of keys like 360 90 30 etc like that to change the direction the teleporter spits you out at.
Than just deselect that, re-select your trigger_teleport with shift + left clicking the brush in the 3d (top right) window, than re-select your teleport_dest and press ctrl+k, You should se a orange line going from the teleporter to the teleport_dest, hope this helps
