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First, which graphics output is recommended? Both Direct3D and OpenGl has a lot of flickers when I move the mouse for some reason, I've experienced similar traits in other DOS games.

Secondly, is there anything that can be mitigated for the slight mouse delay? It's rather annoying.

Thirdly, when I press 1 or 2 to pick an agent alone that command takes more than a second sometimes and sometimes the game doesn't even register my move. I've never had this kind of issue before in any game so it must be specifically with Syndicate.

Anything else that helps a beginner especially regarding controls or any specific dosbox settings that could help with stability or performance.
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It really depends on your system.

For me (Core 2 Duo E8500 @ 3.16GHz, GTX260, 4GB RAM), in my conf file I have output set to overlay and I'm using 12000 cycles. I also play Syndicate in a windowed DOSBox, so fullscreen is set to false. The menu animations are sometimes a little bit fast but the main game runs perfectly.

If your CPU isn't fast enough then you may need to look at putting in some frame skipping to get the right game speed. Use Ctrl+F11 and Ctrl+F12 to lower and raise the cycles whilst the game is running to see if you can find the sweetspot for your machine. In windowed mode the number of cycles is displayed on the DOSBox titlebar.
I noticed I have to run with DDraw, the rest has that flicker issue and I don't know what it is, it's something with my computer and some dosbox games. Not all of them.

I've a Q9550 @ 2.83GHz and according to GOG's system requirements it says 1.8GHz processor, I assume that's single core but not like this game would utilize anymore than that. I'll try changing cycles and see if I can find a sweet spot.

Anything that can be done with the mouse? I've noticed that in my older games particularly dos games the mouse can't diagonally in a smooth way so instead of moving up & right at the same time it moves either right first then up or other way around and it feels really jerky. Not a deal breaker but something I like.
Setting cycles too high can cause slowdown too, and yes, I think DOSBox only utilizes one core, so it is just a case of finding whereabouts to set your cycles for your particular machine. Not too high, not too low.

As for the mouse behaviour, I've never seen that in DOSBox. However, I do know that the Build engine games (Redneck Rampage, Duke Nukem 3D, Blood) have a poor mouselook implementation. It isn't DOSBox, it is actually those games. Some have improved this by using bmouse. Maybe you could try getting the bmouse exe and adding that to the autorun of your DOSBox conf files to see how that works?