Laptop - External Monitor

I use a 27" monitor and a 19" monitor with my laptop because I often need to refer to multiple documents or want to watch Netflix while playing a game. That means I have three monitors, the laptop, the 27", and the 19". Some days I just keep the laptop closed and just use sleep mode. When I tell people I don't use a desktop anymore I usually get "I could never use such a small screen and keyboard", and I reply with "neither could I, and I don't". On to your other questions:

1. In order to utilize 100-120-144 Hz you have to use DVI or Displayport. Most gaming laptops will come with at least one mini-Displayport to take advantage of higher refresh rates. I know MSI even has triple monitor support, if that's something you want.

2. The response time is a stat that is often fibbed. Some monitors that advertise 1ms are really closer to 5ms in reality, or sacrifice picture quality for that refresh rate through a special setting, much like some TVs' "game mode". Check the reviews and pick a highly rated monitor with the right resolution and good color accuracy. A better refresh rate seems better on paper, but in most circumstances you wouldn't be able to tell the difference. Some people swear they can tell the difference between 59 and 60 FPS just like they swear they can tell the difference between 1ms and 5ms refresh rate, but in reality there is such a minute difference. Most of the time it's just in their head, such as when someone has a great monitor on paper that actually doesn't perform at the stated rates when actually tested. I bought a monitor years ago that advertised itself as a 1ms refresh rate without checking reviews and later found out the real refresh rate was ~4ms in the "superspeed mode" because they changed the scale and didn't bother to note it. 60hz vs 144hz is another story. That is more noticeable during movement, which is most of the time during gaming, especially when your FPS drop.

3. HDMI will not cause any kind of delay, it's the primary video output for consoles these days, but it will not allow you to take advantage of the higher refresh rates above 60hz. PC monitors have very little input lag in general, so I wouldn't worry about that, but with TVs you have to use their game mode to reduce input lag. A nice bonus of gaming laptops is you can pick it up and plug it into any screen, a monitor, TV, projector.

My advice would be to shop around a little more for something with a displayport if you want to use a monitor above 60hz, or just save some money and get a 60hz monitor. There is definitely a difference between 60hz and 144hz refresh rate when it comes to movement smoothness, though, so it may be worth the investment. There are some reasonably priced 144hz monitors out there and laptops with displayport are in that price range as well generally.