How can I tell if my parachute will work?

The parachute icon will turn red if it is unsafe to deploy. You can also do it by speed but I don't have the exact safe m/s it is to deploy, I think it's around 250 m/s.

Quote from the wiki:

Changes were made to the staging icons in version 1.0.5.

The staging background colour now indicates whether or not it is safe to deploy the parachute, being light grey when safe to deploy or at rest, a yellow-green colour to indicate that deployment may be risky (at around 250 m/s on Kerbin for main parachutes, nearly twice this speed for drogues) and dark red at any higher speed.

The foreground colour (i.e. the colour of the parachute itself) indicates the state of the parachute, starting at white (unstaged/undeployed) and running through cyan (released but insufficient pressure to semi-deploy), yellow (semi-deployed), green (fully deployed) and bright red (destroyed).

Here is the wiki link with more info on parachutes.

Actually it should be as simple as checking whether there's a button 'Disarm Chute' in parachute context menu.

• If you can disarm it, then you can (and should) disarm it in-orbit and then arm it after de-orbit burn when you get down to subsonic speeds.
• If your chute is armed & deployed (no disarm button) then it will definitely be destroyed by 'aerodynamic forces and heat' during re-entry.