Translation:I know that kanji already.
It's kind of both. Literally it's 'that kanji', but it is often used (e. g. in texts) similarly to the definite article in English. Japanese has no definite article per se. The topic maker wa, and the subject marker ga also function somewhat in a similar fashion. Wa means the speaker thinks the listener knows the phrase marked by wa, and the listener anticipates the parts after wa; ga, on the contrary emphasises the word it maks.
Shirimasu is the polite present simple form of the verb 'shiru', which means 'to know'. Shitteimasu is the present progressive form of the same verb. In english we use the present simple form to say 'I know that', but in japanese the correct use is 'sore wo shitteimasu'. Same goes for the verb 'sumu', to live(somwhere). In english you say 'I live there' but in japanese you will use the form 'sundeimasu' .
知っている is one of those verbs that appears more often in the て-form than in the root form. 知る/知ります on its own is more often used to mean "to learn [something]" or "to come to know [something]", whereas 知っている/知っています is used when you simply "know" something - i.e. the continuous state of knowing it.