Can free plugin on WordPress.org site promote pro-version of this plugin?

In a nutshell – yes, but be careful about it. Detailed plugin guidelines have some related information (emphasis mine):

Trialware is not allowed in the repository. It’s perfectly fine to attempt to upsell the user on other products and features, but a) not in an annoying manner and b) not by disabling functionality after some time period. Similarly, you cannot “cripple” functionality in the plugin and then ask for payment or provide a code to unlock the functionality. All code hosted by WordPress.org servers must be free and fully-functional. If you want to sell advanced features for a plugin (such as a “pro” version), then you must sell and serve that code from your own site, we will not host it on our servers.

So it’s not forbidden, but your free plugin must work by itself.

In general, things like banner or text link advertising should not be anywhere in a plugin, including on its settings screen. […] Putting links back to your own site or to your social-network of choice is fine.

Linking to your general web presence is fine, however pushing unrelated paid products might be considered crossing the line.

About licensing – while you have to host your pro version elsewhere and so .org has not control over it, higher powers have history of nuking people associated with non-GPL products. So the safe course would be to keep things reasonably GPL-compatible to have no issues.

Note that quote from Mika is outdated, plugins must be “GPLv2 or later” compatible to be accepted into repository.