Legolas in the return of the king points out to Gimli that Imrahil was a man of high stature and had elven blood.
So was Imrahil and the men of Dol Amroth southern dunedain?
Yes, Imrahil and the Princes of Dol Amroth were Dúnedain. However, the story of Imrahil's Elvish blood is actually more interesting than that.
History of Middle-Earth has a short discussion about the house of Dol Amroth, where we learn about a marriage between a minor Númenórean lord and an Elf-maid:
Mithrellas, one of the companions of Nimrodel, is lost in the woods of Belfalas, and is harboured by Imrazôr the Númenórean [added in margin: Imrazôr 1950-20761], who takes her to wife (according to the legends and traditions of Dol Amroth); though after a few years she vanishes, whether to wander the woods or seek the havens. The son of the union of Mithrellas and Imrazôr received the elven-name of Galador; from him the lords of Dol Amroth traced their lineage.
History of Middle-earth XII "The Peoples of Middle-earth* Chapter 7: "The Heirs of Elendil"
Another version of this story is told in Unfinished Tales:
In the tradition of his house Angelimar2 was the twentieth in unbroken descent from Galador, first Lord of Dol Amroth (c. Third Age 2004-2129). According to the same traditions Galador was the son of Imrazôr the Númenórean, who dwelt in Belfalas, and the Elven-lady Mithrellas.
Unfinished Tales Part 2: The Second Age Chapter 4: "The History of Galadriel and Celeborn"
Although Imrazôr isn't given a complete family tree, it's a fair assumption that he wasn't called "The Númenórean" because it was a cool name. So Imrahil was indeed descended from the Men of Númenor, although obviously not of as high a station as Aragorn was.
However, his Elven blood is more recent (if you believe the legends of Dol Amroth), thanks to the union of Imrazôr and Mithrellas.
1 of the Third Age, which means Imrazôr died about 900 years before the events of The Hobbit
2 Imrahil's grandfather
Yes Imrahil was a Dunadan of the South although having Elvish ancestry is not the mark of Dunadan ancestry. The Dunedain were a people who were descended from the Edain and became Dunedain due to their struggles against Melkor with the Firstborn in the First Age. Elros who was their first king had elvish ancestry, but all the other Dunedain did not. As time went on Elvish ancestry spread among the people since he had descendants.
In M-E, after the destruction of their homeland of Numenor their lifespans decreased because their land was destroyed and because that's how things happened in Numenor. By the end of the 3rd Age 100 years was about the age at which the Dunedain lived. Aragorn's mother died when she was 100 although she seems to have been depressed at this point so might have died a bit early. However, his line, who were a royal line generally lived between 155-160 years. Other Men still did not live as long even though the lifespan of the Dunedain almost equaled that of other Men. I'd say other Men generally lived to around their 70s. Check the lifespan of the Kings of Rohan for example.
Faramir & Boromir, like the Prince were of elvish descent because they were the Prince's nephews. Their mother was the Prince's elder sister. The Steward's House was related to the royal house via the female line so they also had Elvish ancestry from that side of the family.
Some of the men of Dol Amroth were of Dunedain descent, and it appears most if not all the armed men the Prince came with were. Keep in mind that in Gondor the Dunedain population was small compared to the other non-Dunedain people who lived there. Even when they first established Gondor before the waning of the people through plague and infighting the Dunedain were a small segment of the population. Generally they were found in Ithilien, Dol Amroth, and Minas Tirith for example. The Rangers in the South were from families that used to live in Ithilien and they were Dunedain.
Longevity was a gift given to them & it began to wane the more they looked aghast at their Doom which was mortality. In Numenor as death always preoccupied them and they rejected the elvish way of life their lifespans decreased. This was dramatic in the King's House where the last King of Numenor felt death at his door when he was 200. His father died before he was even 200 years old. However, his cousin the Lord of Adunie from whom the later Kings of Gondor and Arnor descend, lived for over 300 years and died when he was over 320 years old while fighting Sauron.
So death at 100 is not an unusual age for the Dunedain to die at this point in the 3rd Age. Only the Royal line in the North lived longer as I mentioned between 155-160 years. If you look at the last 4 Stewards of Gondor before Denethor only one of them lived to 100. That was Thorondir the 22nd Steward. The Stewards were Dunedain as well. Denethor commited suicide when he was 89 and his father and grandfather died when they were 98 years old.