As a bandwidth-efficient technique, bit-interleaved coded modulation with iterative demapping and decoding (BICM-ID) has attracted much research attention in the field of wireless communication. In this paper, we put forth a joint design of root-protograph (RP) low-density parity-check (LDPC) codes and BICM-ID, referred to as RP-based BICM-ID (RP-BICM-ID), over block-fading (BF) channels so as to boost the throughput under limited bandwidth. To preserve the full-diversity property of RP codes, we propose an efficient modulation strategy for the RP-BICM-ID system by taking the fading-block length into consideration. We also analyze the outage-probability limit of the RP-BICM-ID systems to establish the fundamental lower-limit on their word-error-rate (WER) performance. Moreover, we conceive a multi-level protograph extrinsic information transfer (ML-PEXIT) algorithm to derive the asymptotic WER and bit error rate (BER) of the RP-BICM-ID systems over BF channels. As a further insight, we develop a novel unequal-error-protection (UEP) bit-to-symbol (B2S) mapping scheme for the RP-BICM-ID systems, which gives rise to an additional performance improvement. Analyses and simulations show that the proposed RP-BICM-ID systems can not only realize desirable spectral efficiency, but also obtain near-outage-limit performance over BF channels. Therefore, the proposed RP-BICM-ID systems are very promising in achieving high-reliability and high-rate transmissions under slow-fading wireless-communication environments.