Our customer wants to upgrade from SDL Web 8.5 to SDL Tridion Sites 9.0. We are currently running the DXA 1.8 Java version.
My question is: Can we upgrade to SDL Tridion Sites 9.0 and keep running with DXA 1.8 in the future?
Yes you can. See the following blog (near the end), or the official documentation.
Sites 9.0 (or rather Content Delivery 11.0.0) is compatible with DXA 1.8, however you won't be able to use the new features introduced, for example content mashups.