Priming a beer is the process of adding sugar during the bottling process in order to carbonate the beer. You can bottle condition and carbonate your beer by priming it at the time of bottling with a specific amount of sugar. Using approximately .5 teaspoons ( ½ tsp) of priming sugar per 12oz bottle will provide adequate carbonation for most beer styles.
Typically you will want to prime your beer with corn sugar (dextrose). It is critical that your beer completes its fermentation prior to priming and bottling, as residual fermentable sugars can create excessive pressure in the bottles and cause them to explode. It is also critical that the yeast is still viable so that the priming sugar is converted to CO2 in the bottle, and you do not end up with a flat and overly sweet beer. As in all aspects of brewing, cleaning and sanitation is always paramount. Take special care to ensure that your bottles and caps are clean and sanitized prior to bottling.
Krausen is the foamy and bubbly head that forms on top of beer during primary fermentation. As yeast ferments the sugars in a beer, it creates a great deal of CO2. The Krausen is formed as the CO2 rises to the top of the beer, mixing with proteins, yeast and residues and forming a tall layer of yeast saturated bubbles.
Krausening is also a term for when a measured amount of actively fermenting beer and/or krausen is added to a more thoroughly fermented beer as a means of conditioning or naturally carbonating the beer. Krausening is typically done as a means of carbonating a bottled beer with out violating the German beer purity laws.
Below is a video showing krausen in a 6.5 gallon carboy during primary fermentation.
In very simplified terms, alkalinity refers to the pH of a solution registering greater then 7 and its capacity for neutralizing an acid solution. In order to boost the alkalinity in a mash and offset acidity, you would most commonly add a carbonate or bicarbonate such as chalk\calcium carbonate.