You should have no problem with security and baggage etc at Changi. While there are no priority lanes, there are plenty of automated lanes at immigration. T4 is a separately completely from the other terminals so you will need to take the shuttle bus to T2, they run regularly, just follow the signs. Bag checks are done at each departure gate in Changi.
Re lounges, assuming you have *A Gold status then my advice is to take the airside monorail from T2 to T3 (they go every 4-5 min) and go to the T3 SQ Gold lounge. This is infinitely better than the gold lounge in T2. Just make sure you give yourself enough time to head back to your departure gate in T2. If you are departing from an F gate there should not be much walking as the monorail is near these gates. If you are departing from an E gate then that is on the other side of T2 so a bit of a walk.