life - Notable differences if all stars would disappear except the Sun

There are two main things we should look at here, because there are two main ways these distant stars can affect us: light and gravity.

Light

If all the stars in the universe disappeared (besides the Sun), the most of the luminous objects in the universe would simply vanish. There would still be objects emitting radiation - stellar remnants, accretion disks, etc. - but the notable sources of light would be gone.

Would this be an issue? I can't give you any numbers, but I would assume that there wouldn't be much of a difference. Night/day cycles would continue as normal, because the rotation of the Earth also would not be affected. The behavior of stoma in plants should remain the same, as should all the other natural rituals of life.

Gravity

This is where I'm slightly more concerned. Stars have mass, and so they influence other objects with gravity. There are varying estimates of how much of the Milky Way is made up of stars. For example, McMillan (2011) estimated the stellar mass of the Milky Way to be about 6.43$times$10¹⁰ solar masses, while the virial (total) mass was estimated to be about 1.26$times$10¹² solar masses.

The extra matter consists of gas, dust, planets, stellar remnants, and, of course, dark matter (a lot of it). The mass of the Milky Way would be reduced by about 5% - not a terrible amount, but certainly non-negligible. I don't know how this would impact the motion of the Solar System; detailed simulations based on density models would be needed.

However, any effects from stars wouldn't reach us any time soon. Light and gravity both travel at the speed of light, so we'd have at least four years before we started seeing the effects (4 light-years is the distance to the nearest star, Proxima Centauri). We wouldn't feel the effects from the rest of the galaxy for many more years.