Can I use my tablet while charging?

Generally yes, you can use and charge at the same time as long as the device doesn't get too hot. The tablet will stop charging at 100% automatically, so you don't have to unplug the charger when fully charged.

Most current laptops, tablets and mobile devices use Lithium-Ion batteries. Li-Ion batteries do not suffer from memory effects, and can be recharged many times before showing signs of degraded performance. The worst enemy of Lithium Ion batteries is heat, especially while they are fully charged.

Li-Ion batteries can degrade much faster if they get hot while charging, especially when near 100%. This can even be dangerous in extreme cases. They also degrade much faster if they are routinely completely drained to 0%. The best way to extend the life of Li-Ion batteries is to try keeping them between 40 and 80% charged (most will lose some charge over time by design).

If the usage does not heat up your device much (100% CPU usage tends to overheat some devices), you can keep using it while charging, even though usage consumes some energy, which will extend the charging process.

There is a downside, however. Li-Ion chargers turn off when the battery is full, and charging resumes at some preset drain level. If using the device causes battery drain, this will also cause the charger to turn back on at some point. This may cause mini charge cycles that are not very good for the life of the battery.

General rules about Li-Ion batteries:
Fast-charging degrades lithium-ion batteries faster.
Both heat and extreme cold affect Li-Ion batteries negatively, try to store them at room temperature.
Avoid completely draining batteries to extend their life.
Most batteries drain at about 5-7 percent a month when not in use.
Charging Li-Ion batteries to 85% instead of 100% (and not draining under 20%) can almost double their life.