What initiates primase to add an RNA primer to a DNA strand and what makes it stop adding RNA nucleotides? Is there tags added to the DNA back-bone?
Prokaryotic primases are activated by DNA helicase [1, 2] while the eukaryotic ones are triggered when they form a complex with DNA polymerase alpha and its accessory B subunit .
I couldn't find too much information about what exactly triggers activation, but according to De Falco M et al. (2004):
[...] synthetic function (of the prokaryotic primase) is specifically activated by thymine-containing synthetic bubble structures that mimic early replication intermediates. 
It stops when it finishes reading a DNA template:
The Sso DNA primase utilizes poly-pyrimidine single-stranded DNA templates with low efficiency for de novo synthesis of RNA primers .
- Wikipedia contributors, "Primase," Wikipedia, The Free Encyclopedia, http://en.wikipedia.org/w/index.php?title=Primase&oldid=593928284 (accessed December 1, 2014).
- David N. Frick, and Charles C. Richardson. DNA PRIMASES. Annual Review of Biochemistry. Vol. 70: 39-80 (Volume publication date July 2001). DOI: 10.1146/annurev.biochem.70.1.39
- De Falco M, Fusco A, De Felice M, Rossi M, Pisani FM. The DNA primase of Sulfolobus solfataricus is activated by substrates containing a thymine-rich bubble and has a 3'-terminal nucleotidyl-transferase activity. Nucleic Acids Res. 2004 Sep 30;32(17):5223-30. Print 2004.