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I would suggest Mahjong Tengokuhai, though it's only available on iOS/Android.
I've introduced plenty of my friends who are new to mahjong to that app and they play it regularly so I assume they quite like it. You can set the timer to however long you want. Max is 300 seconds.
When will you be back?
And yep you can. You can either play on [Tenhou](www.tenhou.net/3) or on Mahjong Tengokuhai app in iOS/Android
I have a good one that I use regularly but it's all in Japanese. It's called Mahjong Tengokuhai. If you can read a little bit of hiragana/katakana/kanji it will help tremendously. If not, well you can ask me if you encounter any problem, I'll try my best to help.
You can also try Tenhou.net but it's also all in Japanese unless you install the chrome/mozilla add-on to have it translated to English. The unfortunate thing is that most good clients are in Japanese, so you'll have to bear with that.
That aside, are you interested in playing offline? If you live in Jakarta let's meet up and play!
The third menu from the top is for creating a lobby for playing with friends and you can fill the empty slots with bots.
The rules are extremely similar to Tenhou so once you're confident enough to go against other players you can switch to Tenhou without having a huge detriment to your gameplay.
It's all in Japanese though so if you have any trouble navigating the app feel free to ask.
I use the app from Hangame.
Not sure of the correct translation, but it runs pretty smoothly on my phone. Downside is you have to make an account (for free) to play, and it does require some extra downloading to get fully fleshed. But it has online (which I have yet to test, anyone wanna help?) and single player.
That being said, use what you like, so long as you get to play.
You'll have to deal with the moonrunes though.