Meaning of 'kalapas' What did the Buddha really meant with 'kalapas' (those ultra small particles of existence, that arise and pass away at an incredible speed)?

Is there a correlation between those kalapas and the emptiness of all things (sunnata)?

Can those kalapas be considered as the 'source' for all manifestations?
kalāpa in the sense you are thinking is used in the commentaries. The word is generally used in the suttas to mean "bundle", as in yavakalāpa - bundle of grass, or dhanukalāpa - sheaf of arrows. I can't pinpoint the first usage of the word to mean "smallest particle  of matter", but the Visuddhimagga uses it in this way:


  “But since neither of these is a fact, you should therefore give up conjecturing
  the difference to be in the supporting primary elements. Just as the natures of visible
  objects, etc., are dissimilar from each other though there is no difference in the
  primaries that form a single group, so too are eye-sensitivity, etc., though no other
  cause of their difference exists.”
  
  -- Vism XIV.45 (Nyanamoli, trans)


The Pali here is ekakalāpe - "in a single group". The meaning is that each instance of matter is made up of a single group of characteristics.

The abhidhammattha-sangaha also uses the term:


  Ekuppādā ekanirodhā ekanissayā sahavuttino ekavīsati rūpakalāpā
  nāma.
  
  There are twenty-one material groups inasmuch as they arise together, cease together, have a common basis, and occur together.
  
  (Bodhi, trans)


Bhikkhu Bodhi's explanation is:


  Material phenomena do not occur  singly,  but  in  combinations or
  groups known as rūpakalāpas, of which twenty-one are enumerated. Just
  as all the cetasikas possess four characteristics (see II, §1), so too do
  the material phenomena  in a group. All  the material phenomena in  a
  group arise together and cease  together.  They  have  a common base, namely, the conascent great essentials, which are the proximate cause
  for the derivative phenomena as well as for each other. And they all occur
  together from their arising to their cessation.
  
  (From A Comprehensive Manual of Abhidhamma, pp. 252-3)


Nyanatiloka gives the following explanation of rūpa-kalāpa in his Manual of Buddhist Terms:


  'corporeal group', material unit, designates a combination of several physical phenomena constituting a temporary unity. Thus, for instance, the so-called 'dead matter' forms the most primitive group, consisting only of 8 physical phenomena, called the 'pure eightfold unit' or 'octad' (suddhatthakakalāpa), to wit: the 4 elements (the solid, fluid, heat, motion); colour, smell, taste, nutriment (pathavī, āpo, tejo, vāyo; vanna, gandha, rasa, ojā).
  
  In Vis.M., and elsewhere, it is also called ojatthamaka-kalāpa, 'the octad with nutriment as the 8th factor'.
  
  The simplest form of living matter is the '9-fold vitality unit' or 'life-ennead' (jīvita-navaka-kalāpa), formed by adding 'vitality' to the octad.
  
  Seven decades, or units of ten (dasaka-kalāpa), are formed by adding to the 9-fold unit one of the following corporeal phenomena: heart (physical seat of mind), sex, eye, ear, nose, tongue or body. -
  
  See Vis.M. XVIII, 4; Compendium of Buddhist Philosophy (PTS), p. 164, 250; Atthasālini Tr., II, 413f.


Finally, Mahasi Sayadaw talks about rūpa-kalāpa in the context of rebirth as a human in his discourse on Paticca-Samuppada:


  With the arising of rebirth consciousness there occur simultaneously three kammajā-rūpakalāpas or thirty rūpas. These are rūpas that have their origin in kamma, viz., ten kāyarūpas, ten bhava-rūpas and ten vatthu rūpas. The nine rūpas, to wit, the solid, fluid, heat, motion, colour, smell, taste, nutriment and life together with the kāyapasāda (body-essence) rūpa form the ten kāyarūpas; bhava-rūpa and the solid, etc form the group of ten Bhavūpas. Bhavārūpa means two germinal rūpas, one for manhood and the other for womanhood. 
  
  ...
  
  This embryonic rūpa has the size of a little drop of butter-oil scum on a fine woollen thread. It is so small that it is invisible to the naked eye. It does not exist by itself. We should assume that it arises from the fusion of the semen (sukka) and blood (sanita) of the parents. If we reject this view, it will be hard to explain the child's resemblance to his parents in physical appearance. It is also said in the suttas that the physical body is the product of the four primary elements and the parent's semen. Moreover, the piṭaka specifies three conditions necessary for conception, viz., the parent's intercourse, the menstrual discharge of the mother and the presence of something qualified to become an embryo. Thus it is clear that according to the scriptures, the embryonic kalāla has its origin in the fusion of parent's semen and blood.
  
  ...
  
  According to Western biologists, it is the fusion of the mother's ovum and the father's spermatozoa that gradually develops and becomes a child. The original embryo is so small that it cannot be seen with the naked eye. The findings of these scientists fairly agree with what the Buddhist books say about conception. Without the help of microscope or other instruments but purely by means of his intellect the Buddha knew how life begins with three kalāpas or thirty rūpas as kalāpa on the basis of parents' semen and blood. This was the Buddha's teaching 2500 years ago and it was only during the last 300 years that Western scientists discovered the facts about conception after long investigation with microscopes. Their discoveries bear testimony to the Buddha's infinite intelligence. However, they are as yet unable to reveal the genesis of thirty rūpas probably because the extremely subtle kammajarūpas defy microscopic investigation.




UPDATE (to reflect your new questions):

Is there a correlation between those kalapas and the emptiness of all things (sunnata)?

The theory of the kalāpa has no direct connection with the theory of suññatā; it simply describes the composition of individual groups of matter. Indirectly, though, since suññatā is very much connected with anattā (being devoid or "empty" of self), the fact that rūpa is made up of individual states that arise and cease without remainder is indeed an important part of the realization of this truth. E.g.:


  Having thus discerned by knowledge of contemplation of reflection that
  “All formations are void” (see S III 167), he again discerns voidness in the double logical relation thus: “This is void of self or of what belongs to self” (M II 263; Paṭis II 36).
  
  When he has thus seen that there is neither a self nor any other [thing or
  being] occupying the position of a self's property, he again discerns voidness in the quadruple logical relation as set forth in this passage: “I am not anywhere anyone’s owning, nor is there anywhere my owning in anyone (nāhaṃ kvacani kassaci kiñcanat’ asmiṃ na ca mama kvacani kismiñci kiñcanat’ atthi)” (M II 263).
  
  -- Vism XXI.53 (Nyanamoli, trans)


Can those kalapas be considered as the 'source' for all manifestations?

kalāpa, or more properly rūpa-kalāpa, are physical, so no they are only a source for certain other phenomena. "source" is a problematic term anyway, since the causal nature of reality is far more complex than simply A => B.