Learn Italian: Il mio nuovo corteggiatore è bassino e bruttino. - My new suitor is rather short and plain-looking.

The suffix -ino is a diminutive that generally makes things "smaller." When attached to descriptive adjectives like basso (short) and brutto (ugly), its function is to soften the blow. Instead of a blunt insult, bassino means "on the shorter side" or "short-ish," and bruttino translates closer to "a bit plain" or "unattractive." It makes the description feel less harsh and more conversational.

Could the speaker have used the pejorative suffix -accio here if they really disliked the suitor?

Yes, if the goal was to emphasize how unpleasant he was, the speaker could use a pejorative suffix like -accio. For example, bassaccio would mean short in an ugly or unpleasant way. While bruttaccio exists, brutto is already quite negative, so Italians often simply use the absolute superlative bruttissimo (extremely ugly) or alter the noun instead, like calling him an omacciolo (a nasty little man).

Is corteggiatore used in everyday Italian, or does it sound as old-fashioned as the English word "suitor"?

Unlike the English word "suitor," corteggiatore (from the verb corteggiare, meaning to court or woo) is still frequently used in modern Italian. It is often used playfully or casually in everyday conversation to describe someone who is actively pursuing you, messaging you, or trying to win your affection.