What are the problems that need to be taken in consideration when trying to find planetary position by using jpl ephemerides?
You don't mention what you are trying to access this with but I would strongly recommend AstroPy for handling the ephemeris and handling the co-ordinates and time systems. For your questions:


The Moon and the Earth are both given relative to the Earth-Moon barycenter (center of mass). Separately you can get the vectors from the Solar System Barycenter to the Earth-Moon Barycenter. So if you want SSB->Moon you will need to do two calls to the ephemeris and do vector addition.
It depends how accurately you want things and how fast the thing you want is moving. You can probably use Terrestrial Time (TT) with the ephemeris and you want be horribly off for anything other than Moon. The offset TT-UTC (currently 67.184 seconds) consists of two parts; a variable part from UTC to TAI, currently 37 seconds, which consists (mostly) of the number of leapseconds and a fixed part (32.184 seconds) from TAI to TT. TDB varies around TT by about 2 milliseconds and it's somewhat periodic (dominated by Earth's orbit ellipticity and Jupiter and Saturn) but doing it properly requires a 791 term expansion (see e.g. http://star-www.rl.ac.uk/docs/sun67.htx/sun67ss154.html#Q1-158-946)
Yes, if you want to do anything related from the Earth such as predicting positions of something in the sky, you will need to take the frame bias, precession and nutation into account along with Earth rotation/sidereal time to align the celestial reference frame (ICRS/J2000) with that of the Earth (ITRS).


I recommend USNO Circular 179 (http://aa.usno.navy.mil/publications/docs/Circular_179.php) which has a lot of details of how to do this in the new IAU framework. Meeus's book is very good (I have it also) but is based on the old IAU1984 equator and equinox of date methods.