Thanks for the awesome feedback. Glad you're having fun with this. Here are some answers for you:
I think you may need to reread the way Conversion Beamer's work.

Having at least 1 original weapon wasn't in this update but will be in the next one.
On one turn I couldn't fire a tarantula, all I could do was move. - Was this due to an alien event card, perhaps Weapon jammed?
The assault cannon will only display targets on aliens that you can actually kill. For example, you have 2 Gretchin and 1 Android that are in LOS. You click the "Fire Cannon" button and roll a 1. Targets will appear on the Gretchin but not on the Android as it's armour is too high.
The Tarantula does increase the Armour of the marine however you have spotted a bug with the missile launcher that destroys both the marine and Tarantula. This will be fixed in the next update.
For issues such as BA tarantula marine hanging over the edge of the docking claw, could you please get a screenshot of this when it happens. This will help me trace why this is happening when it shouldn't.
The fusion gun didn't fire through an open bulkhead door - Do you mean a destroyed bulkhead? Did the fusion beam stop at the open door as if it was closed? Did you target an alien past the door or in front of the door? Was the bulkhead a vertical or horizontal door?
The tarantula can be walked over or stopped on if there's no gunner. - will be fixed in next update.
Sometimes the aliens don't move their full rate - This is due to the AI planning a few moves ahead and thinking that the square the alien is on is the best spot for it to be.
I couldn't target an enemy when it was standing next to an open door and I was diganoally adjacent to it and
the open door, but I could still attack it in hand-to-hand. - This is another one of those times that a screenshot of the issue would help me out.
When I used the fire order I couldn't target most of the enemies as before but on the secong shot I could. - Which weapon were you trying to use?
There was a genestealer alien event and two appeared. The next time there was just the one. - That is supposed to happen. That particular mission from the MD book states that this is to occur.
When I used the fire order I was able to move and fire the tarantula. - That is correct. The rulebook states that certain order cards (Fire, Move it & By sections) allow the tarantula to move and/or fire in the same turn. I interpret this to mean that the tarantula fires twice or moves twice with By sections. Fires twice, moves once with Fire! and moves twice and fires once with Move it!
Commander's cannot use the tarantula, only normal marines.
The tarantula can be one side of a closed door and the gunner the other side. - fixed in next update.
There were two dreadnaughts standing next to each other, both in sight but I couldn't get both with the
tarantula and there was no reason I shouldn't have been able to. - I'd need a screenshot to troubleshoot this one.
There was one time when the red targeting circles for the tarantula were dark but I tried shooting anyway and
it worked, so the targeting graphics for the circles don't quite match what you can actually target. - I'll have to look into this one closer as I couldn't replicate it. Which direction was the tarantula facing? On which board? Which firing arc squares did it shoot at?