Klona, I'm afraid that you might have a problem:
Metriaclima lombardoi are a very aggressive species and adults can and will kill each other.
Their environment is also very different from what you appear to have: ideally, their aquarium should have a large quantity of rockwork in it, filling 1/3 to 2/3 of the volume. As a result, they will need powerful filtration to make sure there is even flow through the rocks. Unless your aquarium is in the 4*2*2 ft size, you are very likely to have problems with more than one fish, and by problems, I mean fighting. Those two still look like babies, but then they grow up, the fighting will become tearing chunks out of each other.
Is your aquarium big enough to support them as adults? If not, you should take them back to the shop where you bought them. Please research all fish before you buy them!
In response to your original question, between males, that is usually a show of strength, between a male and female, it is preparation for mating, or a mating attempt.
As for their diet, all they can eat completely in 30-60 seconds, twice per day, is about right. Malawi Mbuna (which is what these are) require a predominantly vegetarian diet, so generic fish flakes won't cut it in the long run.
Here is a good starting point for research on this species: http
/www.cichlid-forum.com/articles/m_lombardoi.php and http
/www.cichlid-forum.com/profiles/species.php?id=798 , you're obviously not the only one who has been caught out with the pretty colours