"Is the letter 'I' always a capital?" When you mean "me, myself", then it is always capitalised. Don't make the learner-mistake of thinking that it is optional.

Yes, when describing yourself.

For engineers 'i' can be a variable for (electric) current. For mathematicians 'i' is the square root of negative one.

letter -- no, word -- yes

There are exceptions, in poetry, for example (see one of my favourite poets from childhood, e.e. cummings, who did not even capitalize his own name!). It also occurs as lower case when texting (without autocorrect), when written by children, or when a writer wishes to de-emphasize his or her own status, or to provoke a reaction in the reader (because it is unexpected and different). It is not considered correct grammar to use lower case 'i' in most other circumstances. This may change over decades or centuries; notice the differences between Germanic capitalization and English, or English and French for example, as well as the tendency in English over the centuries to capitalize fewer and fewer components within sentences.