1) Is mutah marriage allowed with a Shia Muslim girl whom is a non hijabi?

2) Also do you have to ask her questions to make sure she follows religion properly (prays fasts etc) or can you trust her when she tells you she’s Muslim?

3) Can the dowry you gift her be a surprise or does she have to agree on it before hand? Also are prayer beads a valid dowry?

1. It’s allowed. May he she will change to start wearing hijab through Mutah
2. It’s important you know whether she is practicing Muslim or not
3. The dowry has to be an agreement between the two of you. Something of monetary value should be added to make it complete. Obviously base on your capability