I'll just hit the highlights. If you want more information about a particular point just repost but explain in detail what information you need.
Alkali is just another word for base. In chemistry we have acids, bases, and salts (generally although some definitions just recognize acids and bases). An acid is a material, in the simple definition, that provides hydrogen ions in solution. Some common acids are citric (found in fruits such as lemons, oranges, etc) and generally have a sour taste. Tomato juicer is acidic, soft drinks are acid due to the carbonation (carbon dioxide under pressure). Acetic acid is the principal ingredient of vinegar. Most vinegar I see on the market is 4% or 5% acetic acid and there are a number of uses for vinegar in the home but most use vinegar that is dilutd significantly with water. None of those are dangerous, although I wouldn't want to get 5% vinegar in my eye or in an open cut. Other acids I have seen around the house are muriatic acid (another name for hydrochloric acid (HCl) that is not very pure). Muriatic acid is quite dangerous. I have also seen hydrofluoric acid (HF) sold under various trade names for removal of rust spots on carpets. Oxalic acid also removes rust spots and is sold by automotive supply houses for cleaning rust from radiators of automobiles. Both HF and oxalic acid, although not classified as strong acids, never-the-less, are dangerous.
Bases are defined in various ways but the simplest is that they produce hydroxide ions in solution. They are slippery to the touch. Many are common around the house and some are quite dangerous. I'm sure you have seen lye. Lye is essentially sodium hydroxide and it is very corrosive. It will put an eye out in 2-3 seconds. Many drain cleaners are lye (although there are some that are concentrated acids). All drain cleaners are dangerous. Most cleaning agents are mild bases. Chlorox and associated bleaching agents are, for many of them, acids but their danger comes from the bleaching action.
Finally, acids and bases neutralize each other. A common base that can be used to neutralize acids is baking soda. Soda is sodium hydrogen carbonate and it is the material that produces carbon dioxide by reacting with the acid in sour milk (lactic acid) when biscuits are made. Of course baking soda is safe. Another acid found in the home is cream of tartar but that is used in baking also.
I hope this is complete enough to answer your questions but not so wordy as to be overwhelming. Don't hesitate to ask for clarification.