I have sent (epempsa). Epistolary aorist active indicative of pempō as in Eph 6:22.
That ye may know (hina gnōte). Second aorist (ingressive) active subjunctive of ginōskō, “that ye may come to know.” This the correct text, not gnōi (third singular).
Our estate (ta peri hēmōn). “The things concerning us.”
May comfort (parakalesēi). First aorist active subjunctive. Proper rendering here and not “may exhort.”