Yes you can pause it, even in multiplayer.
Simply press space bar to pause the game and give you enough time to choose your card.
Once you choose a card, press continue to play it, and the timer will become un-paused and continue counting down. If you still need more time to think of your other cards, press the space bar after playing each card so that the timer will pause again.
Yes it works online as well, but please don't pause the game for every single card in multi-player, people will most likely become annoyed. Its fine to do it once a turn, figure out what you are going to do, then do it, but I believe you get 60 seconds per main phase in multi-player (or something around that long) which should be enough time to play all the cards you need after you have paused once to think about it.