Plants do no encourage algae growth, however if they come with algae on them and are not 'dipped' before putting into the tank they will continue to grow algae. BBA (black beard algae) is easy enough to remove, look up bleach dipping aquatic plants. [Here's a video]
I followed for my first anubias bleach dip for tips. Anubias is very tolerant to bleach dips, just very thoroughly was it after. To prevent BBA from returning after removal, look at your lighting distance, type, and time on, as well as nitrates and balance of ferts in the tank. Imbalances in these seem to help encourage bba growth.
To answer your other question, yet anubias can be grown emersed (above water) in high humidity environment. Like in the aquarium, the rhizome cannot be buried or it will rot, however you can add aquatic moss on top of the rhizome to help keep it moist. People often use inert clay media and pots of water or smaller tupeprwares with water in a tank for emersed setups. [Here is a site]
that might offer some more tips on setting up an emersed setup. Alternatively if you have a 20g high you can drain 1/2 the water ans sue it as a 10g tank and attach anubias to say driftwood that pokes up out of the water, letting roots reach the water to nutrients (lid is recommended to keep humidity levels up, but a hole(s) is needed to let air vent).