Ok, your tires aren't the perfect size, but they're very close, and they wouldn't cause your speedo to read 60 at 50mph. The correct tire size for 15's on a CRX is 195/50-15.
The non-working tach may be because of a loose connection. The tach signal comes from the blue wire on the far left (driver's) side of the cluster. A new cluster is a good idea, and it's a good time to upgrade too. Since you have a B16, I would recommend this cluster
You can buy them here
, though they're a little bit pricey. Worth it in my opinion, for a cluster that shows the true nature of your engine. It will require a bit of rewiring to work in your 89 dx, but it's not terribly difficult.
A new speedo cable should cure the bouncing speedo, and then the different speedo gear should fix the speedo error. So yeah, looks like replacing those three things should get you all set.
If you decide to get that different cluster, this link
explains how to make the necessary wiring changes for it to work.