As you probably know, the birth of Rama and his brothers was caused by Dasharatha's wives drinking divine Payasa obtained from the fire of the Putrakameshti Yagna (ritual for having sons). As a result, the births occurred very close together, with Rama being just one day older than Bharata, Lakshmana, and Shatrugna, as described in this chapter of the Bala Kanda of the Ramayana:
On completion of the ritual, six seasons have passed by; then in the twelfth month, i.e., in chaitra mAsa, and on the ninth day of that chaitra month [April-May], when it is punarvasu nakshatra yukta navamI tithi, i.e., when the ruling star of that ninth day is punarvasu, for which Aditi is the presiding deity; and when five of the nine planets - sUrya, kuja, guru, shukra, shani are in ucCha sthAna-s, namely, when those planets are in ascension in their respective houses - meSha, makara, karkaTa, mIna, tula - rAshI-s; and when chandra yukta guru, karkaTa lagne - Jupiter in conjuction with Moon is ascendant in Cancer, and when day is advancing, Queen Kausalya gave birth to a son with all the divine attributes like lotus-red eyes, lengthy arms, roseate lips, voice like drumbeat, and who took birth to delight the Ikshwaku dynasty and adored by all the worlds, and who is the greatly blessed epitome of Vishnu, namely Rama....
With the dawn of sun on the next day, fair-minded Bharata is born under Pisces where puSyami is the star of day, later the sons of Sumitra, namely Lakshmana and Shatrughna are born under Cancer, where aaSreSa is the star of the day, i.e., the tenth of chaitra month.
As far as Dasharatha's age goes, when Vishwamitra comes and asks for Rama's help in defeating the demoness Thataka, Dasharatha objects, saying this:
Sixty thousand years have passed from my birth, oh! Vishvamitra, and this Rama is engendered at this age, that too with tribulations, hence taking Rama with you will be inappropriate of you.
This may seem like an astronomically large number, but people in earlier Yugas lived much longer.
Regarding Rama's age when he fought Ravana, in the Aranya Kanda of the Ramayana Sita tells Ravana (who is pretending to be a priest) the ages of Rama and her at the time they were exiled to the forest:
My great-resplendent husband was of twenty-five years of age at that time, and to me, eighteen years are reckoned up from my birth.
Since Rama's 14-year exile ended at about the same time as his battle with Ravana (as discussed in my answer here), Rama was about 39 years old when he fought Ravana.
As far as Lava and Kusha go, Rama and Sita spent 10,000 years ruling Ayodhya before Sita became pregnant, as described in this chapter of the Uttara Kanda of the Ramayana:
Sita and Raghava thus spent their days happily. And thus was spent the delightful winter giving all enjoyments. Enjoying various things the high souled Rama and Sita spent ten thousand years.
Once on a time, having performed all the religious ceremonies, in the fore part of the day, Rama, to spend the evening, entered the inner apartment. Sita, too, having performed all religious ceremonies, at first attended to the service of her mothers in law. Thereupon wearing a beautifully coloured cloth and being adorned with various ornaments Sita appeared before Rama like unto Sachi approaching the king of Devas in heaven. And beholding the auspicious signs of pregnancy in his spouse Rama attained to excessive delight.
Sita went to the forest shortly thereafter, and she gave birth to Lava and Kusha in Valmiki's ashram, as I discuss in this answer. Now while Lava and Kusha were born, Rama's brother Shatrugna was also at Valmiki's ashram on his way to kill Lavanasura the demon who was ruling Mathura. After killing Lavanasura, Shatrugna ruled Mathura for twelve years before paying another visit to Valmiki's ashram, as discussed in this chapter of the Uttara Kanda. And shortly thereafter Rama decided to conduct the Ashwamedha Yagna that would lead to him meeting Lava and Kusha.
So at the time they met, Lava and Kusha were 12 years old and Rama was 10,000 years old.
As far as Ravana goes, his age is never explicitly mentioned in the Ramayana, but for one thing, we know that he engaged in Tapasya for 10,000 years, as I discuss in my answer here. But he's far, far older than that because he actually defeated Rama's distant ancestor Anaranya in battle, as described in this excerpt from the Uttara Kanda of the Ramayana. (Ravana was going around challenging kings to battle to conquer their kingdoms, as I discuss in my answer here.) Now as you can see here, Anaranya ruled Ayodhya 27 generations before Rama. Considering how long people lived back then, that would make Ravana inordinately old at the time of his famous battle with Rama.
Regarding Hanuman, he was born, along with many of the other Vanaras, shortly after Kausalya became pregnant with Rama, as described in this chapter of the Bala Kanda of the Ramayana:
When Vishnu attained the sonship of the great-souled king Dasharatha, then Brahma the self-created addressed all of the gods this way. "Let mighty and guise changing helpmates be procreated to that truth abiding and valorous Vishnu who is the well-wisher of all of us." . When Brahma addressed them thus, those gods have agreed to his order and accordingly started to parent sons in the semblance of monkeys. The direct son of Air-god is the marvellous and adventurous Hanuman with an indestructible body, and one identical in the speed of lady Vinata's son, namely Garuda, the divine eagle vehicle of Vishnu, and among all monkey chiefs he is the intelligent and the indefatigable one too.
EDiT: This chapter of the Prabhasa Kanda of the Skanda Purana says that Ravana ruled for 56.16 million years.