Hey Rivi,
To answer your question, yes, you can run your lappy directly from the AC power source, as long as you are using the original power adapter. Your machine will work just fine but if you don't have a power backup (inverter) installed at your home/office, then your lappy will abruptly shut down whenever the main power supply goes off. If the power failure occurs during trading hours then that could be a p.i.t.a.
Your profile says you are a scalper, so I would suggest that you not to remove the battery if you don't have a good inverter installed at your place.
Now, just in case, you do not have an inverter and you decide to remove the laptop battery, be mindful of carrying out a few trades via the mobile app, as well. Although, almost all brokers have a mobile app these days, the modus operandi and the screen layout may not be exactly the same as you have gotten used to seeing on your laptop screen. So be aware of that and carry out a few trades through the mobile app, lest you punch in an erroneous entry and screw the trade due to the stress associated with day trading.
Another point to consider is that it makes more sense to remove the battery if your laptop is new or is just a few months old. If you use your laptop at one place and don't move around, if really makes sense to remove the battery to extend it's life (less wear and tear of the battery). Make sure the battery is fully charged before you remove it and charge it once every 3-4 months or when ever the battery power drops to 10 percent or so. Any rechargeable battery will naturally discharge over time even if it's not connected. So, don't throw caution to the winds, for a totally discharged battery kept in the cupboard is the last thing you'll ever want.