LTE questions (subcarriers and cyclic prefix)
The FFT size in LTE is defined as 2^(nextpow2(Nsubcarriers/2)+1) or the nearest power of two that is also higher than the number of subcarriers for a given bandwidth. For the 10 Mhz case, for example, this means that 424 FFT bins(1024-600) are zero padded apart including the DC bin. The usual practice is to zero pad the central 423+DC bins and use the rest for filling the data so that you get a continous spectrum of 10 MHz around DC. You can also fill the central 600 FFT bins with data and do a fftshift. See table 1 in this document.
Yes. Each Resource Element(i.e.1 subcarrier and 1 OFDM system in the Time- Frequency Grid) has one QAM Symbol in shared channel.


Check out this visualization to get a better clarity about the LTE resource grid. The resource is allocated both in time and frequency domain and in the case of Multi User MIMO(MU-MIMO) transmission mode, spatial resource allocation of resource elements to different user equipment in the downlink also take place. To keep things simple, let's just focus on a single-antennae transmission. The following diagram will give you a better idea of the whole transmission process.