[incompatible]

I'm not entirely sure what you mean. Do you mean if you have a patent that includes hardware, then that patent would prevent emulating the hardware in software? Wouldn't any software patent then be possible, by the simple expedient of describing it in the patent application as running on a custom single-purpose hardware device?

[TD-Linux]

If you come up with a patentable idea, you can specify its implementation in either hardware or software in the patent (or just be ambiguous). However, if your idea alone is unpatentable, you can't add "implement it in software" to make it patentable, according to Alice vs CLS. Basically, Alice vs CLS removes a certain class of software patents, but certainly not all.

Yes, any software patent is possible by describing it as running on a processor. See for example [1], which has the very common claim prefix of "A machine readable storage medium storing a computer program..." Alice doesn't invalidate these patents unless, by removing that text, the remainder of the claim is unpatentable.

Because software patents are still legal, there's no need to attempt to describe them as running on a custom hardware device - you just specify them as software. Specifying custom hardware would unnecessarily reduce the scope of your claim.

[1] https://www.google.com/patents/US6126544