my ans
1. no penalty
2. you can use your annual leave to offset the notice period if the company agrees
3. if you are serving your notice in your old company, you cannot go to the new one.

Answers
1. No, but normally you will be blacklisted.
2. Company will continue to pay you for the notice period. You can use your annual leave to offset your notice period but subject to your supervisor's approval. (If you can not clear all you AL before you leave, they should encash your leave.)
3. If you use your leave offset the notice period and got approved. You can start in the new company early (It is legislative illegal but usually nobody will care about this.) Salary payed by both company will be taxable (You have to sum up the figures in IR8A form both company.)

需注意一点。
Employment Act没有规定公司必须encash雇员用不完的leave，除非双方的合同上写着。
但一般来说公司都会按人之常情变现给你。
但各位千万得注意，按新加坡的法律，雇主非但可以不把leave转成cash,而且你所积累的leave的有效期只有一年,一年后自动forfeit.

所以要提防一些不要脸的。

非常感谢！
大家good friday!