No, not immediately. As per the scriptures, depending upon his good/virtuous and bad/sinful actions, the jivatama will be taken to Yama and after judgement he will first experience the results of his actions accordingly either in heaven or hell [Agni Pu. - 203.5]. Only after he has experienced those that he will obtain another body on earth.
So to answer the questions 1 and 2, yes it depends upon the karma. More good karma means more time in heaven and hence it will take more time until the jivatma enters another body. Only after their stock of punya is over that they fall down to earth:
te taṁ bhuktvā svarga-lokaṁ viśālaṁ
kṣīṇe puṇye martya-lokaṁ viśanti [BG - 9.21]
When they have thus enjoyed vast heavenly sense pleasure and the results of their pious activities are exhausted, they return to this mortal planet again.
To answer the third question, heaven is a different realm of existence. It's not imagination and to enjoy it means enjoying them there in that specific realm before taking birth here again. Some people say heaven and hell are here only, on this very earth. But apart from this earth there exists other planes of existences and they are not imaginary.
However, I would like to add that heaven, hell and many other realms of existence up to the topmost Brahmaloka, the abode of Brahma, are under the effect and influence of maya. Going there through penance, good action, etc. is nothing but only a waste of time as one has to ultimately return here anyway. Only by attaining the realm of God that one will never have to return and take birth in this mortal plane again. So the Gita says:
a-brahma-bhuvanal lokah punar avartino 'rjuna
mam upetya tu kaunteya punar janma na vidyate [BG - 8.16]
From the highest planet in the material world down to the lowest, all are places of misery wherein repeated birth and death take place. But one who attains to My abode, O son of Kunti, never takes birth again.
In the above post I said that it is a waste of time to go to upper planes of existence through penance, sacrifice, etc. as the end result is only but miserable bondage. But some people like Keshav below don't call it a waste of time. They argue that some people find that path very fulfilling. But Veda calls these kind of people as the supreme fools:
iṣṭāpūrtaṃ manyamānā variṣṭhaṃ nānyacchreyo vedayante pramūḍhāḥ
nākasya pṛṣṭhe te sukṛte'nubhūtvemaṃ lokaṃ hīnataraṃ vā viśanti [Mund. Up. - 1.2.10]
They are but supreme fools who believing the rites ordained by the Vedas
to be the highest, do not understand the other thing
that leads to liberation. They, having enjoyed the fruits of actions in
higher heavens fall down to this world or even to a world lower.
yām imāṁ puṣpitāṁ vācaṁ pravadanty avipaścitaḥ
veda-vāda-ratāḥ pārtha nānyad astīti vādinaḥ
kāmātmānaḥ svarga-parā janma-karma-phala-pradām
kriyā-viśeṣa-bahulāṁ bhogaiśvarya-gatiṁ prati [BG - 2.42,43]
Men of small knowledge are very much attached to the ﬂowery words of the Vedas, which recommend various fruitive activities for elevation to heavenly planets, resultant good birth, power, and so forth. Being desirous of sense gratiﬁcation and opulent life, they say that there is nothing more than this.
There are people of different knowledge and nature who follow different kinds of philosophy. There are fools who do not know what's the best use of time and there are wise who know what's the best use of time. Is it not childish for someone to raise the argument that "It is not a waste of time because the foolish persons do it and find it fulfilling"?
But when I said it a waste of time, I didn't give my own view, I am hardly that wise! I only shared in in short the view of the scriptures as evident from the following verses:
tasyaiva hetoḥ prayateta kovido
na labhyate yad bhramatām upary adhaḥ [SB - 1.5.18]
Persons who are actually intelligent and philosophically inclined should endeavor only for that purposeful end which is not obtainable even by wandering from the topmost planet [Brahmaloka] down to the lowest planet [Pātāla]
evaṁ hi lokāḥ kratubhiḥ kṛtā amī
kṣayiṣṇavaḥ sātiśayā na nirmalāḥ
tasmād adṛṣṭa-śruta-dūṣaṇaṁ paraṁ
bhaktyoktayeśaṁ bhajatātma-labdhaye [SB - 7.7.40]
It is learned from Vedic literature that by performing great sacrifices one may elevate himself to the heavenly planets. However, although life on the heavenly planets is hundreds and thousands of times more comfortable than life on earth, the heavenly planets are not pure [nirmalam], or free from the taint of material existence. The heavenly planets are also temporary, and therefore they are not the goal of life. The Supreme Personality of Godhead, however, has never been seen or heard to possess inebriety. Consequently, for your own benefit and self-realization, you must worship the Lord with great devotion, as described in the revealed scriptures.
I am not adding other verses that also share the view to lengthen the post, as from this update I hope I made it clear that it is not my personal view that going up only to return later and get entangled in karma in various life forms is only a waste of time.