- The fork is "right" if it has the right "sag", that is, if it lowers a bit when you get on the bike. The right sag is no less than 10%, no more than 25% of total travel, for a regular bike (non-downhill, non-special-purpose);
- Basically three "areas" must be addressed on maintenance:
- Cleaning the inside, for removal of old oil/grease, water, mud, grime, rust, etc.
- Caring for the damping elements, which could be elastomer, coil, air chamber, open oil bath, etc. That would vary a lot depending on the type;
- Lubing the telescopic parts, which are responsible for the movement of the fork. Depending on the type (open oil bath, for example) the damping oil and the stanchion-lubing oil is the same, so it is serviced together.
- This is called "preload", and probably increases or decreases the compression of a coil spring or elastomer. That is for the adjustment of "sag" according to your weight, being equivalent to say that it lets the fork "harder" or "softer".
As far as I know, the brand of your fork is on the cheap end of the quality spectrum, so it's possible that it doesn't work perfectly, or at least not as perfectly as higher-end models. I'd say that, if it "works", meaning if it saves your body (hands mostly) from shaking over bumps, then keep it, even if it has too much sag, or some play, or is not so light. But if it "gives up" working too soon (say, you go over bumps and it barely moves, or you feel the bumps hard on your hands), than it is well worth to change it for a better model.
If you decide you'll keep it and service it yourself, I'd recommend purchasing some grease/oil (check which you'll need for your specific model) that's made specifically for bike suspension. A lot of lubricants I've inadvertedly used in the past contained some sort of adhesive (to stick to the metal surfaces and protect them), and the lubrication became gluey as soon as the bike hit some dusty path. On the other hand, fluids intended for suspensions or hydraulic systems tend to expel impurities and keep flowing nice over time.
EDIT: I've found some photos and reviews online, of your fork (search words: "sync 266 fork"). By that (plastic upper caps, dust "accordions" around the telescopes) and by the reviews description (mtbr.com), I'd say it is a low-end fork, thus without any hydraulic valves inside, most probably elastomer or coil spring. You should be able to disassemble it at home "no-fear".
Hope this helps!