How deep the drain pipe bury under the cement floor

I am helping a friend to build a bathroom and toilet in a old house basement, Waterloo, Ontario. It is a low basement and we wanted to run the drain pipes under the cement floor.
How deep shall we dig to lay the drainage pipes?

I think the operative question here is how deep is the main sewer line? You need to run 1/4" per foot slope from where the pipe turns horizontal to where it connects to the main drain line outlet. Depending on where that is, how far you have to go, and how deep it is will somewhat determine.

If the PVC sewer pipe is 4" dia +3" cover= 7" deep.
How about the "u" joint for the toilet? and the distance from the main approximate 10 feet away, the slop?

I am afraid to dig too deep that might hit something, such as a gas line??

What is a "U" joint for a toilet? If you are thinking of a P trap, toilets have their trap built in, so that is not a consideration. Or are you thinking of the closet bend that connects to the flange? That is just a special type of elbow and require no extra depth. You have to add 1/4" per foot depth for the slope. If there is a gas main, the gas company will locate it for you, just call them. There should not be a gas main buried under the floor. Have you planned for venting this toilet? I wonder if you may be into something beyond your experience level. It might be time to have a plumber in to evaluate the job. It might save you and your friend a lot of time and money in the long run.

As to the length, just take say that 10' x 0.25"/foot, and you come up with 2.5". In other words, the low end needs to be at least 2.5" lower than the higher end of the horizontal portion. As to how high a closet bend is, I'm not sure; I'd have to either measure one or find the spec. You still need to know the height where you can actually connect that new run into the main sewer line...hopefully, you have enough drop so you can maintain at least the minimum required slope.

If you have any concerns about hitting any utilities... you should be calling the utility companies before you start digging, get them to come in and locate / mark the locations for you.

I've never heard of any utility running under a basement floor, though.

Gas, electric, and water usually all come in through a basement wall somewhere. Find them before you start.