For SGS T-bills and MAS Bills, during an auction, there are cut-off, median, average price/yield?

Depends on whether you submitted a competitive or non-competitive bid. https://www.mas.gov.sg/bonds-and-bills/investin...

Non-Competitive Bid
In a non-competitive bid, you only specify the amount you want to invest, not the yield. Choose this if you wish to invest in the bond regardless of the return or are unsure of what yield to bid.

You will get the bond at the cut-off yield, which is highest accepted yield of successful competitive bids.

All non-competitive bids will be allotted first, up to 40% of the total issuance amount. If the amount of non-competitive bids exceeds 40%, the bond will be allocated to you on a pro-rated basis.