Is it safe to run laptop straight to the sucket without battery on it?

Yes, it's okay to do that since your battery is already damaged. My laptop is only 1year and 3 months old and it's battery is already malfunctioning. In the sense that it discharges so fast. The time I bought this, I'm already removing the battery and plugging it directly to the power source. But I guess it weakened the life of my battery being stocked at one place.

i think yes.. if your battery situation like that, why you must use your battery?

If you have the UPS turned on, it's okay but without it, it is rather risky, especially when the electricity is suddenly cut off, it may distroy the hard disk.

I am Doing the Same things before 6months ago. I think it's the Better idea to without replace the Old better Idea. But it's the Bad idea may be to change new Laptop parts, some time Power failure make sudden off of the Computer it's not Safe for the Ram and hard disk it cause some Problem. My laptop now having some issues i think that may be occured because of that reason. So Please be Safe about the issue.

The use of battery in laptops is for you to able to use it outdoors, and of course when power source suddenly stops you have your battery which doesn't interrupt your files from closing all of a sudden. Thats the main use of the battery...and with your question, yes indeed, it is safe to plug in directly without the battery, the only problem you might encounter is when you have trouble with power source, and your files will be corrupted. The best thing for you to do is to buy another battery maybe two so you have extra, it would be a big help when you use your battery too much in order for it not to overheat.

Yes its safe, after time the battery will lose charge, you just need to purchase a new battery online,

Yes, you could. The power cord isn't just for the charging of the battery. And running your laptop using direct current from the socket wouldn't harm your unit. The only drawback of this is you lose the portability of the laptop. It's just like you're using a desktop now.

Yes, it's advisable to do it that way actually. Most battery got spoilt or have shorter battery life because they were overcharged. However, I'm not sure if your computer heats up because of your battery. It may be due to your fan collecting dust so you may need to clean up your fan as well.

It's not insane. In fact it's a good thing to do. A technician once advised me to remove the battery of my laptop when i'm just at home so as to conserve the battery. So what you're doing is right.

Yes, in fact I always remove the battery when I plug the laptop, because I have heard having the battery on while it's on charge and the battery is 100% that is one of the most common things that make it break. Idk if its true, but just in case.

Actually, it is always a good idea to use your laptop without battery on when you can use power plug. This helps you to keep your battery in good condition. If you use both at the same time, your battery life will reduce significantly which renders it totally useless after some time. You should always use battery only when you are out. Because battery allows you to have mobility. While you shouldn't use the power plug during bad weathers as your laptop may burn down.

As the others here stated, that is a good thing to do, it makes your battery last longer. However, I suggest when you do use your laptop, you don't plug it into the socket. Always use a surge protector or UPS(Uninterrupted power supply) and plug it into that. A power surge or outage can damage the device quite a bit, especially with the battery removed.