Note: I'll take about time travel and causality violation, but what I mostly mean is the creation of Closed Timelike Curves. These are the things you use to go back and kill yourself before you travel through time, and are generally considered to be a bad thing.
Wormholes, by themselves, do not necessarily violate causality. You can induce a time difference between one end of the wormhole and the other (by flying it around at relativistic speeds) but various theories suggest that when you try to use this construct a time machine (by moving temporally separated wormhole mouths close to each other) you get Interesting Effects which cause the wormholes to collapse. For more information, read up on Hawking's Chronology protection conjecture and structures such as Roman rings, but for now you can just assume that in a Universe with chronology protection, you can't violate causality with a network of wormholes.
Wormholes in this sort of friendly universe are relatively safe. Such wormholes are shortcuts through spacetime, but light travelling through them still behaves as you might expect and you don't get the kind of issues that "real" FTL travel or signalling might cause. The price you have to pay is that wormhole mouths get moved around at sublight (but possibly relativistic) speeds. This means that the initial journey between two stars takes many years, but subsequent ones are faster.
Teleportation, if it allows travel faster than lightspeed, will ruin all that. All bets are off. Chronology protection in the presence of FTL travel and signalling is a vastly more complex affair. Creating a wormhole where the two mouths are already widely separated (eg. one end is near a different star, or even planet) is effectively teleporting things around and has the same problems.
It is possible to conjure up a universe where FTL does not result in time travel, perhaps as a result of the existence of a privileged reference frame, but discussion of such things are a bit outside the scope of this question. Given the relativity seems to be a real thing, adding special frames like this in a hard scifi setting is likely to be awkward. You might reasonably assume that all soft scifi settings have one of these magical reference frames, even assuming they cared about relativity in the first place, which they probably didn't
Now, with regards to wormholes:
Would a traveler come back home after the exact time he spent on another planet or would he be too late? If a portal was kept open between two planets would time be a constant?
Wormholes link points in spacetime. When you travel through a wormhole, you have travelled in both time and space. If the two mouths of the wormhole were "stationary" relative to each other, then if you travelled through the wormhole, waited 5 minutes and travelled back, you'd arrive 5 minutes after you left, plus however long the journey through the wormhole took (which you could handwave to be more or less instantaneous, but is likely to take a finite amount of time).
If one end of the wormhole was travelling at high speeds relative to the other end, clocks would of course tick at different rates at either end of the wormhole. You could travel out to a relativistic starship, wait a while, but when you've returned more time will have passed at your origin than you spent at the destination.
If a portal is closed and then opened again will time have passed into another century?
It depends how you re-open the wormhole. If you had to create a new wormhole and then fly one mouth to a distant star, then even if you flew it at high relativistic speeds relative to the source many years will pass before it arrives at its destination. If you were in a universe with chronology protection, this is a safe thing to do, and no time travelling will occur.
If you shrunk a wormhole down to impassibility but kept the mouths in place, you could re-inflate it later and it would be as if it had been left open during the intervening time.
If you can teleport the wormhole faster than light, all bets are off, because this is FTL and that means you're in grave danger of time travel. It is up to you what happens then, because all bets are off.
I can recommend reading the Orion's Arm setting article, Wormholes - A Layman's Guide, for a setting with safe wormholes and a decent amount of thought put into the science behind the whole thing.
Another setting is The Verge by Luke Campbell, which also has some hard-sciency wormholes but with fewer restrictions than Orion's Arm. Scrolling down to the wormhole section in the setting's technology blurb, or reading the shorter bit on wormhole warfare might be interesting.
