When programming I use ie and eg It's informal, probably technically wrong, but it's readable, and unlikely to propagate some badly closed filename five lines up in my code. Periods are too important to flaunt about carelessly.
A common variant is ie. instead of i.e.. Contrast with e.g. which is from the Latin exempli gratia meaning "for example." One can construct sentences where either one is acceptable, but usually just contemplating the English meaning of each and picking the best fit is the way to go. If you're referring to Internet Explorer, just say Internet ...
When a writer uses parentheses to define a phrase or clarify a word in a sentence, is it appropriate also to use i.e. in the parentheses? That use seems redundant to me.
You need to use e.g. in your example because the list is not complete e.g. exempli gratia - for example i.e. id est - that is viz. videlicet - that is sc. scilicet - namely (see viz) In contradistinction to i.e. and e.g., viz. is used to indicate a detailed description of something stated before, and when it precedes a list of group members, it implies (near) completeness.
