Here the duration 5 weeks means your parents must entry singapore within 5 weeks. Once they arrive in singapore, how long they can stay up to the visa issued at custom.

在进入新加坡的海关处，官员会给批多少天呢？是不是还是可以批30天（机票是30天的），然后父母进来后，马上去延期一个月。这样可以吗？
eith 14 days or 30 days, it depends...no relation to your ticket.

延期是不是只有3个月和5年的两种？
once your parents are in singapore. You can take them to ICA to extend the visa. the 5 years one means long term social visa...

PR替父母办签证还需要押金吗？
Mostly no... but it depends.