How does Emotional Intelligence go along with Dhamma practice? Emotional intelligence is an ability to deal with one's emotions. I am wondering how does it affect and get affected by the practice of the Dhamma? Does deeper meditative absorption lead to heightened awareness and control of one's emotions and vice versa or are they completely unrelated? Also, does the 'feeling' skandha include feeling of one's emotions? Are there any wholesome emotions one feels as the practice deepens? Are the Brahmaviharas all there is to wholesome emotions?
The Abhidhamma is useful for this question. I quote from The Abhidhamma in Practice by N.K.G. Mendis.
Starting from the top:

The Abhidhamma deals with realities existing in an ultimate sense,
called in Pali paramattha dhammaa. There are four such realities:

Citta, mind or consciousness, defined as that which knows or experiences an object. Citta occurs as distinct momentary states of
consciousness.
Cetasikas, the mental factors that arise and occur along with the cittas.
Ruupa, physical phenomena, or material form.
Nibbaana.


Next we go into the cetasikas:

The second reality or paramattha dhamma is the cetasikas. The
cetasikas are the mental factors or concomitants that arise and perish
together with consciousness (citta), sharing its object and basis.
The Abhidhamma lists 52 kinds of cetasikas. One is feeling (vedanaa),
another is perception (saññaa). The remaining 50 are grouped together
under the term sa&quot;nkhaaraa.

And then we go into sa&quot;nkhaaraa:

Sa&quot;nkhaaraa is a collective term for the other fifty cetasikas. These fall into four groups:

Universal mental factors (sabba citta saadhaaranaa)
Particular mental factors (paki.n.nakaa)
Unwholesome mental factors (akusalaa)
Beautiful mental factors (sobhanaa)


There are 7 universal mental factors (including feeling and perception) and 6 particular mental factors. These are neutral:

The universals and particulars are, in themselves, ethically
indeterminate but become wholesome, unwholesome, or neither, depending
on the state of consciousness in which they occur.

There are 14 unwholesome mental factors and 25 beautiful mental factors.
The four Brahmaviharas are included in the list of 25 beautiful mental factors. Others on the list include mindfulness, faith, non-attachment, shame of evil, fear of evil, right action, right speech, right livelihood, wisdom etc.
The lists are very long, so I will let you take a look at it on the website yourself.

OP: I am wondering how does it (emotional intelligence) affect and get affected by the practice of the Dhamma?

With Dhamma practice, the unwholesome mental factors should become weaker and the beautiful mental factors should become stronger or more dominant. This is the increase of emotional intelligence that comes with the practice.

OP: Does deeper meditative absorption lead to heightened awareness and control of one's emotions and vice versa or are they completely
unrelated?

Your ability to consciously identify and eliminate unwholesome mental factors, and consciously apply beautiful mental factors, increase with the Dhamma practice, including meditation. You get more control over your mind, so to speak.

OP: Also, does the 'feeling' skandha include feeling of one's emotions?

The feeling aggregate is sensing the six sensory media, which includes thought and mind. Emotions are a kind of thought. So, yes.
But unlike externally originated sights, sound and smell which you cannot control, thoughts come out of your mind in a process chain described in this answer. So, you can control it through increasing emotional intelligence.

OP: Are there any wholesome emotions one feels as the practice deepens? Are the Brahmaviharas all there is to wholesome emotions?

No. As shown above, there are 25 wholesome mental factors including the four Brahmaviharas. So, Brahmaviharas are not all there is to wholesome mental factors.