Is it considered ultimate to be reborn as a human?
In Hinduism, it is considered ultimate to be not born at all. Jivas being part of God exist in different kinds of bodies starting from insects and humans on earth to gods and demons in heaven and hell. But any kind of such material existence being under the influence of repeated death and birth, has always condemned by the scriptures and saints. That is why the scriptures prescribe ways like jnana and bhakti for attaining moksha, mukti, etc. But because only through the human body that moksha can be attained, it is considered the best among the bodies. So even the gods of heaven want human birth so that they can achieve liberation:
svargiṇo ’py etam icchanti lokaṁ nirayiṇas tathā
sādhakaṁ jñāna-bhaktibhyām ubhayaṁ tad-asādhakam [SB - 11.20.12]
The residents of both heaven and hell desire human birth on the earth planet because human life facilitates the achievement of transcendental knowledge and love of Godhead, whereas neither heavenly nor hellish bodies efficiently provide such opportunities.
Other births being bhoga yoni, their actions can not award liberation. Only the human birth being a karma yoni can award spiritual results as per the action.
Is the human birth the result of past good deeds?
It depends. One may have got the human birth because he did good things (mixture of good and bad) in the past life or he may have got it in course of time after going through other form of bodies. The rule is simple as below:
A person when does only good works as prescribed in the scriptures he goes to higher planets like heaven. When a person does bad and sinful works prohibited by the scriptures, he goes to hell. When a person does a mixture of good and bad, he reborns on earth in different kinds of bodies as per his action. [SB - 4.29.26-29]
One who does sinful actions, goes to hell and after experiencing punishments there obtains lower animal forms and gradually obtains a human birth in course of time. [VP - 2.6.34]
One who does good and scripture prescribed actions goes to heaven and returns down to earth once his merits are exhaust. [BG - 9.21]
Why do some lament while some request for a human birth?
As you see from the above references, human birth is kind of a middle stage between good and bad, some lament why they did some bad work and sins that they had to take birth as human and experience difficulties, otherwise they could have been gone to heaven. But those people do not have the correct knowledge. Those who do, instead pray to God for human birth so that they can practice devotion, austerity, etc. to get permanent liberation from repeated death and birth. So the scriptures say:
nṛ-deham ādyaṁ su-labhaṁ su-durlabhaṁ plavaṁ su-kalpaṁ guru-karṇadhāram
mayānukūlena nabhasvateritaṁ pumān bhavābdhiṁ na taret sa ātma-hā [SB - 11.20.17]
The human body, which can award all benefit in life, is automatically obtained by the laws of nature, although it is a very rare achievement. This human body can be compared to a perfectly constructed boat having the spiritual master as the captain and the instructions of the Personality of Godhead as favorable winds impelling it on its course. Considering all these advantages, a human being who does not utilize his human life to cross the ocean of material existence must be considered the killer of his own soul.
iha cedavedīd atha satyamasti na cedihāvedīn mahatī vinaṣṭiḥ [Kena Up. - 2.5]
- If during this life one understands the supreme, then it’s good. But if one fails to understand the Supreme, then he’ll incur a great loss.
Because this human birth has this potential to set one jiva free from samsara, obtaining the human birth is nothing but the grace of God. (कबहुक करि करुणा नर देहि । देत ईश बिनु हेतु सनेही - RCM). One just needs to utilize it for the right purpose.
Does a jiva attain moksha from any life form?
No, almost always not except some exceptions. This question has an answer here which says moksha is possible only through the human birth. I have heard an example of how God realized souls can give moksha to animals as mentioned in that answer. There was a cow in Shri Ramana Maharshi's ashram and at the time of the cow's death he placed his hand over her and said she was liberated. So those are only few exceptions. Another thing is that, an individual attains heaven only by doing good deeds, moksha or liberation from births is the result of following the paths described in the scriptures.