Is there a downside to signing up for credit cards to get their sign-up rewards? Can i get the rewards and close account 1 or 2 years later?

There isn't really much of a downside for signing up for those credit cards in order to get the free gifts. Do note that even if you cancel immediately after receiving the free gifts, there is a waiting period of approximately 12 months before you are considered as a new-to-bank customer again.

You should also watch out for cards with mandatory annual fee payments, such as Amex KrisFlyer Ascend and most Visa Infinite cards. Most cards can get their annual fee waived pretty easily, and even if you can't, they typically let you cancel without needing to pay the fee.

I suggest that you take advantage of the sign-up promotions, and keep the card(s) that align best with your spending patterns and rewards goals (cashback/miles). The DBS Live Fresh Student card is rather restrictive with the $500 credit limit and does not enjoy some of the benefits that standard cards do.

To add on you also risk annual fees which you may not be able to waive without any transactions. Increase chances of not paying fees if you forget and end up paying more.

Penny wise, pound foolish.

Since you are planning to use the DBS Live Fresh Student Card, I am assuming you are a currently a student. Both credit cards require an annual income of $30,000 for Singaporeans/PR which may not be achievable for you at this stage.

Assuming the requirements for the card application are met, I would personally still not apply for the card just for the reward as the time could be put to better use.