Screen content coding (SCC) is an extension to High Efficiency Video Coding (HEVC) used to compress screen content videos. Besides the conventional intra (INTRA) mode, new coding tools, intra block copy (IBC), palette (PLT) modes, and adaptive color-space transform (ACT) are introduced to encode screen content (SC) such as texts and graphics. However, the use of IBC, PLT and ACT increases the encoder complexity though coding efficiency can be improved. While there were numerous approaches for fast INTRA, fast IBC and fast PLT at coding unit (CU) level, we propose fast prediction unit (PU) decisions for INTRA and IBC. In addition, fast ACT approach is also proposed. Both approaches reduce the encoder complexity of SCC by making use of SC characteristics, neighbor correlations, and intermediate cost information via random forest (RF). Experimental results show that, with also fast CU mode decision approaches at CU level, our proposed approach, namely HoFastRF, can obtain 51.29% average encoding time reduction with only 1.45% increase in Bjontegaard delta bitrate (BD-rate). It is the first fast SCC approach to obtain over 50% average encoding time reduction with less than 1.5% increase in BD-rate.