Syphilis is transmitted through sexual actions through small cuts, for malaria, it would have to be through mixing of blood from a contaminated source to a uncontaminated source.
There is 50% probability that their daughter's son will have the disease, because daughter chromosomes are XX , and the X from father will have x- linked disease, now in next generation the son will have XY chromosomes, Y is from father and X will from mother, now mother have two "XX", out of these two one carry x- linked disease, that means 50 percent chances of having disease in son.
In the lyric cycle, the virus attaches to the host cell which then injects its DNA. By using the hosts cellular metabolism