Generally, no, Lake Malawi cichlids don't do well with live plants. Generally, they're a rock fish, so they need lots of rockwork that provides caves and hiding spaces (mbuna in particular). There are a couple hardier species of plants that can sometimes work with some of the species, but it depends on which species.
Lake Malawi cichlids are basically broken into three groups - mbuna, haps, and peacocks. Mbuna are the real rock fish that need tons of it, while haps and peacocks are a little more open-water fish, but you'll still need some rocks and caves.
There are literally hundreds of species in Lake Malawi, so to give you any more help really, you're gonna have to narrow it down
Like when you ask about how many you can keep...Malawi cichlids range from about 3-4" to over 2 feet in length. As you can imagine, exactly which species you choose will determine how many you can keep - not only is size a factor, but aggression, temperment, dietary needs, and compatability with others are even more important when choosing a stocklist.