When a rift opens does a gate and rift both open at the same place?

Rifts don't interfere with open gates: both can be at the same location. Rifts don't make gates appear though.There's no interaction between gates and rifts.

Rifts can appear in sealed locations as well. A rift that enters play is only activated on the next turn it moves.

If a rift opens as a result of a Mythos card with no gate, you draw cards from the Mythos deck until you get a card with a gate location shown, and you put the rift on that gate location. But this is rare: most Mythos cards that don't open gates have all the dimensional symbols on them, and for the rift to open, the symbols pattern must match exactly.

Okay, I didn't answer this properly, but I think I've covered most of the scenarios with rifts.

Yes, but does a gate and a rift open at the same place at the same time? Or does a rift open instead of the gate?

Rifts and gates are independent of each other. They can appear at the same place and at the same time. You simply put one on top of the other, or one next to each other.A rift doesn't replace a gate or vice versa. They can peacefully coexist.

Musha Shukou said:

Refer to the resolution of Mythos card. The first step is the gate opening. So, if a new gate opens, take the marker and place it on the showed location. Then put the clue(s) on the board, if possible. Then you have the monster movement resolution phase. This phase can make a rift to be opened. In this case look at the lower left corner of the Mythos card and see where you have to place it. As Zealot said, no interference at all