Taking your points individually:
1) Today guns and missiles can be offensive/defensive. And, as we know today and throughout history, SOME things might work well as dual-purpose (88mm is a great example - anti-tank, artillery and anti-aircraft...even navalized versions), but it's not a universal answer. And, in the example of the 88 - not without changing out shells. So while the cannon remained the same, mounts and shells and even training was different for each variation. A CIWS or SeaRAM is far more effective at anti-missile defense than a rapid-fire 5' gun. Each has their purpose and each excels in different areas - though they can both be employed to shoot at small craft. So yea, Traveller falls within the same concept.
2) A 500 Dton craft is not exactly "agile", and a 1/12 Dton missile is far more agile. I don't see how agility means anything here.
3) I don't know what you are hinting at here unless you are talking about a ship not having any restrictions on mounting ground-weaponry vs. regular ship weaponry. If that's the case, then yes, players will abuse the hell out of it.
4) As I see it the mixed turret was to try to give smaller ships a little of everything. When you have only 1 hardpoint you want to try and cover all your bases.
5) Placement of defensive weaponry is going to be based upon field of fire. But since you can't guarantee you'll only engage the enemy from one vector, ships have to be able to engage in all directions, thus your weapon mounts are predicated upon mission and tactics. For general defense you'd want 360 degree coverage. Generally speaking you try to give yourself the best arc coverage you can. Like a naval ship, starships still have a bow, stern, port, starboard, dorsal and ventral sides.
6) For most point defense, it's going to be all computer-controlled anyways. An operator would prioritize longer-distance, or vague guidelines like torpedoes vs missiles. Beyond that its going to be too fast for a person to intervene and your system will use pre-programed guidelines. That's no different than it is today.
7) For point-defense, a gatling laser makes a lot of sense. A pulse laser, in theory, could do the same, by altering the emitter and releasing more bursts with less energy per burst. But that's never how the books have described them.
8) Grouping your point defense together is a bad idea. One hit and you lose them all. Plus you miss out on coverage. You are better to put them as overlapping.
9) The video is interesting, but logically the spin doesn't give the ship much of an advantage. It's PD cannons were spread around the ship, giving it arcs of fire. The cannons apparently were in continuous fire mode, thus rotating the ship didn't give you advantages - at most it would pass off firing solutions to another cannon. And the missiles were all coming from the same ship inbound, thus they all shared the same attack vector. While it looks cool, it is tactically pretty much meaningless.