Using NASDAQ high frequency trading (HFT) and minute-by-minute Limit Order Book (LOB) data over 120 sample stocks in 10 weeks between 2008-2010, including the week of the Lehman Brothers crisis, we study how trading activities of HFTs, NHFTs (Non-HFTs) and their order placements interact, and affect overall market quality. We capture order placements via the depth (step) and the height (price) dimensions along the LOB. We first document that HFTs are active not only at the top of the LOB, but their orders are placed along the LOB with an average around the 5th step, slightly ahead of NHFTs who on average are close to the 6th step. Generally, both HFTs and NHFTs are more aggressive in order placement with large stocks and hidden orders and HFT orders are further ahead during the crisis week, though price-wise they all back off somewhat with more conservative placements by NHFTs. In market turmoil, whenever HFTs see NHFTs trade among themselves, they become less aggressive in order placement. However, when HFTs trade, other HFT orders become more aggressive by moving ahead. On the contrary, NHFTs generally become more aggressive when other NHFTs supply liquidity in trading, and more conservative when HFTs are the supplier. We find mixed results on the impact of HFTs order placements and trading activities on market quality by different measures, but aggressive orders by HFTs and NHFTs both are related with decreases in short-term market volatility. Our findings highlight the importance of not only studying HFTs and NHFTs activities along the LOB, but also in both depth and height dimensions, instead of only at the market inside quotes.