A few marriages between Betazoids and non-Betazoids have produced children, the best known of whom is Lt. Cmdr.  Deanna Troi of the USS Enterprise-D. Children of mixed marriages generally do not get as high a telepathic ability as do full-blooded Betazoids. Lt. Cmdr. Troi only has empathic abilities, although she can communicate telepathically with other Betazoids.  The University of Betazed being galactically renown for psychology studies is an assumption.  Because of their training in the schools of Betazed, they are rarely xenophobic, and can communicate with most any other race at their level. 

Because of the unique structures (or shields) of Ferengi, Dopterian, Breen, and some others minds, Betazoids cannot read anything. 

With the exception of their telepathic abilities, Betazoids are essentially similar to humans in all other respects.

Betazoids are able to communicate non-verbally with each other and with other telepathic species (telepathy). This capacity can be used to detect the thoughts and intentions of others (receptive telepathy), or to send out thoughts and signals (projective telepathy). 

Also, Betazoids can communicate via emotion (empathy). Empathy is described as the ability to detect another being's emotional state (receptive empathy), and the ability to signal one own's emotional state to others (projective empathy).

The thoughts and/or emotions received or sent can be anything from shallow, surface thoughts to deep, subconscious states. They also have the ability to use a technique similar to a Vulcan mind-meld. This requires preparation, but not actual physical contact.

Betazoids can forge extremely strong telepathic links with each other, and with many other telepathic species, and so communicate with them in a totally non-verbal way. Some species, notably humans, can forge a partial mental link to a Betazoid or half-Betazoid. This normally requires a strong emotional involvement (example: Deanna Troi and Will Riker).

There are many species that are resistant to Betazoid telepathy, notably the Ferengi, Dopterian and the Breen. The Ferengi and Dopterians are resistant to telepathy due to their four-lobed brain, while the Breen have a completely different brain structure to the Betazoids and most humanoids. Also, Betazoids cannot "read" the minds of animals, because animals have highly chaotic and random minds. 

Betazoids can use their mental abilities without touching their target. They can also use their abilities without seeing their target, but in this case the telepathic contact is not as good (the readings are confused, or contact is only temporary etc.) There are also several factors that can reduce or incapacitate the ability of Betazoids to "read" others. Some of these factors are:
1. Environmental interference
2. Strange energy fields
3. Using mental abilities through large amount of substance, like rock
4. Trying to read large number of minds at once
5. Injury or illness in the Betazoid
6. Combat or highly stressful situation
7. Extremely strange, bizarre, or unusual minds

Betazoid culture prizes honesty and ethical values.   Betazoids, much like Vulcans, do not lie. They also consider it unethical to read other people's minds unless invited to do so. The Betazoid ambassador Lauxanna Troi is somewhat different in her approach to this, she tends to read people's minds uninvited, generally causing embarrassment for all concerned.  Mrs. Troi aside, Betazoids do not pry into people's minds unasked. Unasked, the most they would normally do would be a light empathic probe, which would detect another beings surface emotions. Anything more than that must be done for a very good reason, and, if at all possible, with the consent of the target.

Full Betazoids are both telepathic and empathic.  Half-Betazoids are not telepathic, they can only use empathy.