1.    The expression «Être (adjective/past participle) de» translates as "to be (adjective) to", so «Je suis désolé de »  translates to "I am sorry to" 

2. être en retard - be late

Putting the 2 parts together «Je suis désolé d'être en retard» (d'être is the contraction of de + être).

This sentence is a little confusing because, both in English and French, the same verb appears both in conjugated form and then as the infinitive - another example may help "You are happy to see me" - « Tu es content de me voir »

https://www.lawlessfrench.com/grammar/verbs-with-de/

Yes, you can say 'Je suis en retard' - 'I am late'. Alternatively 'Je vais être en retard' or 'Je serai en retard' - 'I am going to be late' or 'I will be late'.  Not quite the same meaning though.