Are this subpanel's neutral and ground connected?
It is wrong. The neutral and ground (from the supply feed) are connected and that's wrong. But what's worse is it doesn't appear to be bonded to the panel.  That means the grounds have no path back to the main panel.   You need to move the ground from the feed (the twisted silver wire) to one of the ground bars attached to the panel (don't bond the neutral to the panel ground). That would fix the worst of the mistakes here.  I also don't see any noalox compound on the aluminum wires, but it may be there, just not visible. Without noalox, Aluminum wires are subject to corrosion, which leads to bad connections, which leads to over-heating.
If you decide to fix this before replacing the panel, be sure to turn off power to it at the breaker in your main panel.