Learn Romanian: Am ridicat ceașca aburindă de cafea. - I raised the steaming cup of coffee.

The base gerund form is aburind (steaming), which normally doesn't change. However, when a gerund is used as an adjective to describe a noun, it has to agree with that noun in gender and number. Since it describes ceașca (feminine singular), it takes the feminine ending -ă.

What is the root verb of aburindă and how was the base gerund formed?

The verb is a aburi (to steam or to fog up). To form the gerund of verbs ending in -i, you drop the final -i and add the suffix -ind, which gives us aburind. Most other verbs take the suffix -ând.

Could we change the word order and say ceașca de cafea aburindă?

You could, but it changes exactly what is being described. Because cafea is also a feminine singular noun, placing aburindă at the very end makes it grammatically attach to the coffee rather than the cup. The current word order keeps the adjective right next to ceașca, keeping the focus on the cup itself.

Why doesn't aburindă have a definite article on it, since we are talking about the steaming cup?

In a standard Romanian noun-adjective pair, only the first word gets the definite article. The noun ceașcă (cup) comes first, so it takes the article to become ceașca. The adjective aburindă just agrees in gender and number but doesn't take its own article.