Is my laptop at risk now?  

Bree said:

There is no advantage in removing the battery while on AC as the charging circuit will turn off all charge to the battery (even a trickle charge) once it reaches 100% capacity.

Anyway, on many current laptops you can't without removing the base cover first, so it's a moot point.

In that case, why a lot of sayings that we should keep the battery off from the laptop separately when we put away the laptop for long time.

Tsw88 said:

In that case, why a lot of sayings that we should keep the battery off from the laptop separately when we put away the laptop for long time.

Ah, that's a different case. You first asked about removing the battery while on AC power. Now we are talking about putting the laptop away for a long time.

When installed in a laptop there will be a very small drain on the battery, even when the laptop is 'turned off'. There is always a very small amount of power supplied to the circuits for the power switch (it's not a true 'switch', it just triggers the power circuitry to power up the rest of the hardware). Some laptops may have a higher drain than others when powered off. Your laptop has already proved itself as safe for over a year's storage with the battery installed, so I wouldn't worry about that too much.

For long-term storage a Li-Ion battery is best stored with a state of charge (SoC) of 40%-50% and kept cool (less than 25°C). More on that here...

Table 2 illustrates the remaining capacities of lithium- and nickel-based batteries after one year of storage at various temperatures. Li-ion has higher losses if stored fully charged rather than at a SoC of 40 percent...

BU-702: How to Store Batteries Battery University
.

Bree said:

Ah, that's a different case. You first asked about removing the battery while on AC power. Now we are talking about putting the laptop away for a long time.

When installed in a laptop there will be a very small drain on the battery, even when the laptop is 'turned off'. There is always a very small amount of power supplied to the circuits for the power switch (it's not a true 'switch', it just triggers the power circuitry to power up the rest of the hardware). Some laptops may have a higher drain than others when powered off. Your laptop has already proved itself as safe for over a year's storage with the battery installed, so I wouldn't worry about that too much.

For long-term storage a Li-Ion battery is best stored with a state of charge (SoC) of 40%-50% and kept cool (less than 25°C). More on that here...

BU-702: How to Store Batteries Battery University
.

My laptop actually comes with two battery, one is removable, another one is real internal, not removable. It's x250 Lenovo. What is the advantage of having two batteries? I forget why I picked
this, it was a quick sale purchase, I did not look into details....

btw, I am not very worried about the battery lifespan, I am more worried that it's said over time the Li battery could blow up itself internally, I know it's a dangerous even if I have no knowledge of Chemistry, by common sense.

Does nowadays Li battery blow up itself? Or does it only apply to extreme cases like extreme temperature or moisture or intentionally hit

Tsw88 said:

Does nowadays Li battery blow up itself? Or does it only apply to extreme cases like extreme temperature or moisture or intentionally hit

Design/manufacturing faults can cause fires, remember this? Samsung Galaxy Note 7 - Wikipedia

But you'd have found out long ago if that applied to your batteries. For good quality batteries they are only a risk when they are abused.

With more than a billion mobile phones and computers used in the world every day, the number of accidents is small. By comparison, the National Oceanic and Atmospheric Administration say that your chance of being struck by lightning in the course of a lifetime is about 1 in 13,000. Lithium-ion batteries have a failure rate that is less than one in a million. The failure rate of a quality Li-ion cell is better than 1 in 10 million.

Safety Concerns with Li-ion Batteries - Battery University

Bree said:

Design/manufacturing faults can cause fires, remember this? Samsung Galaxy Note 7 - Wikipedia

But you'd have found out long ago if that applied to your batteries. For good quality batteries they are only a risk when they are abused.

Safety Concerns with Li-ion Batteries - Battery University

I am not only concerned about my current laptop. I also want to learn for the future. Then the next time I will take care my laptop better.

Now the laptop was bought 3 years ago and only used less than 10 times and the last time I took it out was 1.5 years ago. Now the laptop has a lot of problems, Windows does not Update. It's stuck at "Checking for Updates" forever. I tried some commands provided by other websites. It returns with result suggesting that the integrity of the current Windows is bad, and so I'll probably need to clean re-install the system.

Not turning ON the computer for a year, I thought it was only sleeping, I thought everything was alright, but now looks like it will give out a lot of problems. I've spent a few hours in the past few days to troubleshooting a lot of things...

Tsw88 said:

...the laptop was bought 3 years ago and only used less than 10 times and the last time I took it out was 1.5 years ago. Now the laptop has a lot of problems, Windows does not Update. It's stuck at "Checking for Updates" forever...

Well, that at least is not the battery's fault

Rather than a clean install which would remove all non-Microsoft apps (including all the OEM utilities, customisations and drivers) try a factory reset which will put it back to OEM factory specs.

Reset Windows 10 | Tutorials

Alternatively (or in addition) try an in-place repair upgrade which would also bring you up to date by installing 1809.

Repair Install Windows 10 with an In-place Upgrade | Tutorials