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All of the animations I see show the heat shield detaching and falling to the ground, then Insight detaching and landing. There is no information about what happens with the upper part of the heat shield and the parachute. What if it lands on Insight?

I'm pretty sure it will be like the Phoenix lander. Collectively that part of the lander is referred to as the "Backshell". This is the image of Phoenix of the hardware on the surface.

This is mentioned in the official timeline.

Powered Descent - Once the lander separates from its backshell and parachute, 12 descent engines on the lander begin firing and the onboard guidance software slows down the spacecraft until touchdown.

During the parachute descent, InSight's trajectory is at an angle to the vertical. After the backshell and parachute separate, the engines fire, leveling the craft. This allows some horizontal separation between the parachute and the craft:

11:52 a.m. PST (2:52 p.m. EST) — Activation of the radar that will sense the distance to the ground

11:53 a.m. PST (2:53 p.m. EST) — First acquisition of the radar signal

20 seconds later — Separation from the back shell and parachute

0.5 second later — The retrorockets, or descent engines, begin firing

2.5 seconds later — Start of the "gravity turn" to get the lander into the proper orientation for landing

22 seconds later — InSight begins slowing to a constant velocity (from 17 mph to a constant 5 mph, or from 27 kph to 8 kph) for its soft landing

11:54 a.m. PST (2:54 p.m. EST) — Expected touchdown on the surface of Mars

12:01 p.m. PST (3:01 p.m. EST) — "Beep" from InSight's X-band radio directly back to Earth, indicating InSight is alive and functioning on the surface of Mars

https://mars.nasa.gov/news/8390/nasa-insight-landing-on-mars-milestones/

Also of note:

InSight controllers have been receiving daily weather updates of the Elysium Planitia landing site from NASA’s Mars Reconnaissance Orbiter – allowing controllers the chance to upload last-minute tweaks to the timing of InSight’s parachute deployment and activation of its landing radar system to account for landing-day weather characteristics.

Of note, InSight was also designed to be able to land during a Martian dust storm – something it will not be required to do Monday but was nonetheless baked into the craft’s design given that, once launched, the science platform’s landing date and time were fixed and could not be postponed.

https://www.nasaspaceflight.com/2018/11/nasa-mars-fleet-insight-landing-red-planet/

An explanation of the landing and a comparison with Phoenix is available at NASA's Insight Entry, Descent and Landing webpage, but it doesn't answer your question as clearly as NASA's LiveStream video of Insight's landing at 13:18.

At an altitude of one mile the lander falls away from the back-shell and lights it's engines, then it rotates away so the back-shell doesn't come down and hit it.

The failed landing of the ESA Schiaparelli is shown on the JPL webpage: "PIA21131: Closer Look at Schiaparelli Impact Site on Mars - "the parachute deployed as planned but was released (with back shell) prematurely, and the lander hit the ground at a velocity of more than 180 miles per hour (more than 300 kilometers per hour)".

Despite coming in far too quickly there is excellent separation between the pieces as shown in this photo (click to zoom):

"At lower left is the parachute, adjacent to the back shell, which was its attachment point on the spacecraft. The parachute is much brighter than the Martian surface in this region. The smaller circular feature just south of the bright parachute is about the same size and shape as the back shell, (diameter of 7.9 feet or 2.4 meters).

At upper right are several bright features surrounded by dark radial impact patterns, located about where the heat shield was expected to impact. The bright spots may be part of the heat shield, such as insulation material, or gleaming reflections of the afternoon sunlight.".

A later photo taken by the High Resolution Imaging Science Experiment (HiRISE) camera on NASA's Mars Reconnaissance Orbiter observed shows: "Schiaparelli Impact Site on Mars, in Color".

Since the Insight lander was able to send back a test photo I conclude that the heat shield did not strike it and it wasn't covered by the parachute. A photo of the landing site from HiRes may be forthcoming.