Why is it useful to know the type of data a variable holds?
Often the data type of a variable constrains what you can do with it. For example, you can't perform array-related functions on simple strings. Similarly, you may want to make sure that a variable contains an integer or a float before using it in a mathematical calculation, even though PHP will often help you by changing types for you in this situation.
Should I obey any conventions when naming variables?
Your goal should always be to make your code easy to read and understand. A variable such as $ab123245 tells you nothing about its role in your script and invites typos. Keep your variable names short and descriptive.
A variable named $f is unlikely to mean much to you when you return to your code after a month or so. A variable named $filename, on the other hand, should make more sense.
Should I learn the operator precedence table?
There is no reason that you shouldn't, but I would save the effort for more useful tasks. By using parentheses in your expressions, you can make your code easy to read while defining your own order of precedence.