Took my car for mot at weekend and on route to the station these faults started to happen

1. When driving petrol gauge goes to empty then when stationary goes bk to the correct level.

2. When ive been driving every now and then when stopped at lights car starts hunting, like i say not all the time????.

3. car passed mot but seems strange during emissions it never hunted, but on the way there and on the way home it did, any answers would be greatly received.

Thanks Steve