Learn Farsi: حسِ خوبی دارم.

In Farsi, when a noun and an adjective are connected by the -e sound (the ezâfe), the indefinite suffix -i attaches to the very end of the whole phrase. So, instead of attaching it to the noun, it goes at the end: hes-e khub-i (a good feeling).

There is a small diagonal mark under the word hes (حسِ). What does that indicate?

That symbol is a kasre. It represents the short -e sound that connects words together, known as the ezâfe. It links hes (feeling) to its adjective khub (good). Farsi writers often leave this mark out in daily life, but it is written here to help you pronounce the phrase as hes-e.

Does this phrase mean "I feel good" physically, or "I have a good feeling" like an intuition?

It usually implies having a good intuition or a positive vibe about a situation. If you want to say that you physically or emotionally "feel good," Farsi speakers more commonly say hâlam khub e (my condition is good).

Why isn't the word for "I" (man) at the beginning of the sentence?

The verb dâram (I have) ends with the personal ending -am, which already means "I". Because the verb makes it perfectly clear who is having the feeling, the independent pronoun man is optional and is usually dropped in natural conversation.