How to perform multiple actions with one button of a button panel

You can't, big conveyor doors must be connected to other big conveyor doors. Same goes for the small ones.

Best thing you can do in that picture above is to rotate the cargo container 90 degrees to the left or to the right, so that the big opening is facing towards the connector. Then place a big conveyor with it's small doors to the top and bottom so the big doors are connected to the connector and cargo container, while at the same time the other 2 remaining big doors are on it's sides. Then remove the conveyor tubes you've placed now and place them on the conveyor cube's sides, then reconnect the blocks you had connected with the tubes before moving them.

Also tip: Small conveyor doors CAN'T move components (steel grids, large steel tubes, etc), they only allow access for Oxygen, equipment (tools, guns, ammo) and ores/ingots (small amounts at a time). Large conveyor doors can move every component and can move ores/ingots at a larger amount at a time.

The sole of a landing gear is indeed not suitable for a projector to place a block on.

There are lots of ways to do this, but I'd probably do something like this:

I created this schematic only from top view nor did I draw the whole torpedo, but it should suffice. The're 2 torpedo shafts here: The top one is the actual torpedo, while the bottom one is a dud with a decoyblock in it. I would place the decoyblock as the first block in front of the engine.

The projectorblocks can be placed anywhere outside of the shafts, you can adjust the position of the projection in the controlpanel of the block itself (till a certain range, but the range is pretty big). And ofcourse the welders need to be connected to your conveyor network.

When you have done all this, you can place timerblocks anywhere on your ship. You need to program the chains of each timerblock, which will be the most time consuming. You'll need to chain timerblocks together so it does a lot of actions automatically:

2 timerblocks to override the thrusters on both torpedoes to ignite the thrusters and also they should activate the next 2 timerblocks to release both torpedoes (the dud should be released a little earlier than the actual missile). The timerblocks that released the the torpedoes should then activate 2 more timerblocks to turn on the welders to create new torpedoes and finally activating another set of timerblocks to finally turn them back off after a few certain amount of time. Make sure to name the timerblocks properly so you can distinguish them from each other in the controlpanel (for example TimerStartWelderDud and TimerStartWelderTorpedo).

This should be working as a fairly simple torpedo launcher mechanism. Just make sure the projections of both missiles have 1 block of free space on all sides except where the mergeblocks should connect each other. And also make sure the shaft is long enough that the torpedo engines won't burn a hole in it.