Expression of plasmid genes
It would depend of the plasmid, the genes it contains and the promotors those genes have. Basically, regulation of extrachromosomal genes follow the same patterns of the rest. Bacteria, Archaea and some other organisms that can have plasmids will express the genes if the promotors of those genes are constitutive, or if they trigger by conditions that are present in a given moment. The degree of expression would be a function of the characteristics of the promoter and the number of copies of the plasmid. Finally, the number of copies of the plasmid would depend of its size and the characteristics of its replication origin.

Organisms can loss the plasmids if doing so don't suposse a negative effect (this is a big problem in industrial microbiology, since the recombinant strains may be unstable and reduce its productivity). In laboratory, a plasmid containing resistance genes towards an specific antibiotic would remain stable as long as this antibiotic is present in the media. The characteristics of its replication origin also play a big role determining the stabilty of plasmids. You can even select for the loss of plasmids, take the example of URA3 in Saccaromyces (not a bacteria, but the mechanisms are the same), wich can be used as a negative selection factor if the media contains 5-fluoroorotic acid.

So there's no particular advantage in expressing plasmidic genes all the time. When that happens, actually there exist an evolutionary pressure against the presence of the plasmid, and thus it trends to dissapear. Bacteria can survive without plasmids (with the exception of some that carry megaplasmids that acts more than little chromosomes. In some of this cases, the plasmid may contain genes for important methabolic pathways and other key elements of the cell, thought if the genes they carry are very importants, like polymerases or ribosomal RNAs, the term minichromosome is prefered). However, plasmids may contain genes that confer an important advantage to the population (like in presence of an antibiotic), and if so the plasmid spread. If at some point the ecological pressure cease, the plasmid would turn unstable again. Note that it's not impossible to have horizontal genes transfer between plasmid and chromosomes, and plasmids (alongside viruses and foreign transformed DNA) are important sources of new genetic material.