How do I increase my cycling duration or distance limits? I am a student thus hardly get time to go on tours or hiking! In an average I cycle around 6-10 km per day but in holiday times I go for a trip around the city on my MTB for around 100km ride and trying my best to decrease the time required.

However I rode for 200km recently and I am worried about any chance of physical damage for going on long tours without regular practice? Are there any restrictions on total hours or distance of continuous cycling?

N.B: I am having a pull in my Achilles Tendon and it hurts!
As to your initial question, there are no hard, general limits.

Listen to your body and don't push yourself if anything starts hurting. If something (like your Achilles tendon) hurts only afterwards, that's also a clear sign you overdid it and you should note what you did so you can go a little easier next time. Of course also wait with your next tour until nothing hurts anymore.

The issue when your whole body is really exhausted as Daniel says should only arise when you overdo it a lot and/or don't eat/drink enough. In my own experience, you will notice that you feel stupid and very simple things like going through a roundabout and taking the right exit will suddenly seem as difficult as a math problem and eventually (not in my own experience, luckily) you will faint.  As long as you are looking out for the signs of this, really I don't think anything bad should happen. Just don't push yourself too much. If you reach this exhausted state, you might feel pretty bad (in a general way, tired, mostly) for several days.

Some proper high-calorie sports drink should help to keep your body running if you don't eat enough, but there is a limit (raised by training) on how much your body can metabolize so sooner or later you'll still run into the above issue.

The question was edited to make the question more about how to raise said limits. I don't actually have a lot to say about this. It will go up by itself the more you train, it's as simple as that. Regularly go to your limits, but not beyond them (or not too far). You will improve.

Personally my way to do this is to just use your bike for all the travelling where it's at all possible. Commute all year round. Visit a friend or parent 50km away? Maybe you can go by bike (and use their shower). Need groceries? Go by bike.