Yes, T-shirt is correct.
It is not necessary to capitalise the 't' in t-shirt. It is not a proper noun, but just a common noun. Capitalisation is not necessary even though the t-shirt was so named because it resembles a capital T.
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No, "T-shirt" should not be capitalized unless it is at the beginning of a sentence. It is a common noun and not a proper noun.
No, the word "smartphone" should not be capitalized unless it is at the beginning of a sentence.
No, the word "epitaph" should not be capitalized unless it is at the beginning of a sentence or part of a title.
The word "banker" should not be capitalized unless it is at the beginning of a sentence or part of a title.
No, the word "rif" is not always capitalized. It should only be capitalized if it is part of a proper noun or at the beginning of a sentence.
No, the word "fifteen" should not be capitalized in a date within a sentence unless it is the first word of the sentence.