Regulation in plants bearing cleistogamous and chasmogamous flowers
This is a very good question, but I think the reason that it's not being answered is because it is in a sense too broad: different plant groups maintain balances of cleistogamous and chasmogamous flowers, and they modulate that balance through different mechanisms. Many of these mechanisms (genes involved, environmental cues, developmental pathways) may not be fully understood.

Culley and Klooster (2007) categorize cleistogamy depending on the degree to which "the prevailing environment has a say":


In dimorphic cleistogamy CL and CH flower differ in the time or place
of production, with CL flowers produced in conditions (underground,
low light levels, early in the season) that are potentially
unfavorable for outcrossing.
In induced cleistogamy potentially CH flowers that experience conditions such as drought or low temperatures fail to open and self-pollinate, becoming, in effect, CL flowers.


You should check out the Culley and Klooster (available online if you make a jstor login) – they discuss complete cleistogamy which addresses your last question. They report several completely CL species in their Table 1, and give references.

More generally, many different plant groups maintain balances of self-pollination and outcrossing (i.e. "real sex"), through an even more diverse set of mechanisms.

Even more generally, many plants and some animals maintain balances of sexual reproduction and clonal reproduction, through an even more diverse set of mechanisms. For instance, vegetative reproduction (e.g., strawberry runners) is very common in many plant groups; facultative and obligate parthenogenesis in animals also occurs.



Culley, Theresa M. and Matthew R. Klooster (2007). The Cleistogamous Breeding System: A Review of Its Frequency, Evolution, and Ecology in Angiosperms. Botanical Review. Vol. 73, No. 1, pp. 1-30